Electrons in Atoms and the Periodic Table PDF

9: ELECTRONS IN ATOMS AND THE PERIODIC TABLE  CHAPTER OVERVIEW 9: Electrons in Atoms and the Periodic Table 9.2: Light- Electromagnetic Radiation 9.3: The Electromagnetic Spectrum 9.4: The Bohr Model - Atoms with Orbits 9.5: The Quantum-Mechanical Model- Atoms with Orbitals 9.6: Quantum-...

9: ELECTRONS IN ATOMS AND THE PERIODIC TABLE  CHAPTER OVERVIEW 9: Electrons in Atoms and the Periodic Table 9.2: Light- Electromagnetic Radiation 9.3: The Electromagnetic Spectrum 9.4: The Bohr Model - Atoms with Orbits 9.5: The Quantum-Mechanical Model- Atoms with Orbitals 9.6: Quantum-Mechanical Orbitals and Electron Configurations 9.7: Electron Configurations and the Periodic Table 9.8: The Explanatory Power of the Quantum-Mechanical Model 9.9: Periodic Trends - Atomic Size, Ionization Energy, and Metallic Character 9.E: Electrons in Atoms and the Periodic Table (Exercises) 9: Electrons in Atoms and the Periodic Table is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 1 9.2: Light- Electromagnetic Radiation  Learning Objectives Define the terms wavelength and frequency with respect to wave-form energy. State the relationship between wavelength and frequency with respect to electromagnetic radiation. During the summer, almost everyone enjoys going to the beach. Beach-goers can swim, have picnics, and work on their tans. But if a person gets too much sun, they can burn. A particular set of solar wavelengths are especially harmful to the skin. This portion of the solar spectrum is known as UV B, with wavelengths of 280-320 nm. Sunscreens are effective in protecting skin against both the immediate skin damage and the long-term possibility of skin cancer. Waves Waves are characterized by their repetitive motion. Imagine a toy boat riding the waves in a wave pool. As the water wave passes under the boat, it moves up and down in a regular and repeated fashion. While the wave travels horizontally, the boat only travels vertically up and down. The figure below shows two examples of waves. Figure 9.2.1 : (A) A wave consists of alternation crests and troughs. The wavelength (λ) is defined as the distance between any two consecutive identical points on the waveform. The amplitude is the height of the wave. (B) A wave with a short wavelength (top) has a high frequency because more waves pass a given point in a certain amount of time. A wave with a longer wavelength (bottom) has a lower frequency. A wave cycle consists of one complete wave—starting at the zero point, going up to a wave crest, going back down to a wave trough, and back to the zero point again. The wavelength of a wave is the distance between any two corresponding points on adjacent waves. It is easiest to visualize the wavelength of a wave as the distance from one wave crest to the next. In an equation, wavelength is represented by the Greek letter lambda (λ). Depending on the type of wave, wavelength can be measured in meters, centimeters, or nanometers (1 m = 10 nm). The frequency, represented by the Greek letter nu (ν ), is the number of waves that 9 pass a certain point in a specified amount of time. Typically, frequency is measured in units of cycles per second or waves per second. One wave per second is also called a Hertz (Hz) and in SI units is a reciprocal second (s ). −1 Figure B above shows an important relationship between the wavelength and frequency of a wave. The top wave clearly has a shorter wavelength than the second wave. However, if you picture yourself at a stationary point watching these waves pass by, more waves of the first kind would pass by in a given amount of time. Thus the frequency of the first wave is greater than that of the second wave. Wavelength and frequency are therefore inversely related. As the wavelength of a wave increases, its frequency decreases. The equation that relates the two is: c = λν The variable c is the speed of light. For the relationship to hold mathematically, if the speed of light is used in m/s, the wavelength must be in meters and the frequency in Hertz.  Example 9.2.1: Orange Light The color orange within the visible light spectrum has a wavelength of about 620 nm. What is the frequency of orange light? Solution Solutions to Example 9.2.1 Steps for Problem Solving Example 9.2.1 9.2.1 https://chem.libretexts.org/@go/page/47514  Steps for Problem Solving Example 9.2.1 Given : Identify the "given" information and what the problem is asking you Wavelength (λ) = 620 nm to "find." Speed of light (c) = 3.00 × 10 8 m/s Find: Frequency (Hz) List other known quantities. 1 m = 10 9 nm 1.Convert the wavelength to m. 2. Apply the equation c = λν and solve for frequency. Dividing both Identify steps to get the final answer. sides of the equation by λ yields: c ν = λ 1 m −7 620 nm × ( ) = 6.20 × 10 m 9 10 nm Cancel units and calculate. 8 c 3.0 × 10 m/s 14 ν = = = 4.8 × 10 Hz −7 λ 6.20 × 10 Think about your result. The value for the frequency falls within the range for visible light.  Exercise 9.2.1 What is the wavelength of light if its frequency is 1.55 × 1010 s−1? Answer 0.0194 m, or 19.4 mm Summary All waves can be defined in terms of their frequency and intensity. c = λν expresses the relationship between wavelength and frequency. 9.2: Light- Electromagnetic Radiation is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 9.2.2 https://chem.libretexts.org/@go/page/47514 9.3: THE ELECTROMAGNETIC SPECTRUM  LEARNING OBJECTIVES Know the properties of different types of electromagnetic radiation. Electromagnetic waves have an extremely wide range of wavelengths, frequencies, and energies. The highest energy form of electromagnetic waves are gamma (γ) rays and the lowest energy form are radio waves. The figure below shows the electromagnetic spectrum, which is all forms of electromagnetic radiation. On the far left of Figure 9.3.1 are the highest energy electromagnetic waves. These are called gamma rays and can be quite dangerous, in large numbers, to living systems. The next lower energy form of electromagnetic waves are called x-rays. Most of you are familiar with the penetration abilities of these waves. They can also be dangerous to living systems. Humans are advised to limit as much as possible the number of medical x-rays they have per year. Next lower, in energy, are ultraviolet rays. These rays are part of sunlight and the upper end of the ultraviolet range can cause sunburn and perhaps skin cancer. The tiny section next in the spectrum is the visible range of light. The visible light spectrum has been greatly expanded in the bottom half of the figure so that it can be discussed in more detail. The visible range of electromagnetic radiation are the frequencies to which the human eye responds. Lower in the spectrum are infrared rays and radio waves. Figure 9.3.1: The electromagnetic spectrum, with its various regions labeled. The borders of each region are approximate. (CC BY-NC-SA; anonymous by request). The light energies that are in the visible range are electromagnetic waves that cause the human eye to respond when those frequencies enter the eye. The eye sends a signal to the brain and the individual "sees" various colors. The highest energy waves in the visible region cause the brain to see violet and as the energy decreases, the colors change to blue, green, yellow, orange, and red. When the energy of the wave is above or below the visible range, the eye does not respond to them. When the eye receives several different frequencies at the same time, the colors are blended by the brain. If all frequencies of light strike the eye together, the brain sees white. If there are no visible frequencies striking the eye, the brain sees black. The objects that you see around you are light absorbers—that is, the chemicals on the surface of the object will absorb certain frequencies and not others. Your eyes detect the frequencies that strike your eye. Therefore, if your friend is wearing a red shirt, it means the dye in that shirt absorbs every frequency except red and the red frequencies are reflected. If your only light source was one exact frequency of blue light and you shined it on a shirt that was red in sunlight, the shirt would appear black because no light would be reflected. The light from fluorescent types of lights do not contain all the frequencies of sunlight and so clothes inside a store may appear to be a slightly different color when you get them home. SUMMARY Electromagnetic radiation has a wide spectrum, including gamma rays, X-rays, UV rays, visible light, IR radiation, microwaves, and radio waves. The different colors of light differ in their frequencies (or wavelengths). 9.3.1 https://chem.libretexts.org/@go/page/47515 9.3: The Electromagnetic Spectrum is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 9.3.2 https://chem.libretexts.org/@go/page/47515 9.4: The Bohr Model - Atoms with Orbits  Learning Objectives Define an energy level in terms of the Bohr model. Discuss how the Bohr model can be used to explain atomic spectra. Electric light bulbs contain a very thin wire in them that emits light when heated. The wire is called a filament. The particular wire used in light bulbs is made of tungsten. A wire made of any metal would emit light under these circumstances, but tungsten was chosen because the light it emits contains virtually every frequency and therefore, the light emitted by tungsten appears white. A wire made of some other element would emit light of some color that was not convenient for our uses. Every element emits light when energized by heating or passing electric current through it. Elements in solid form begin to glow when they are heated sufficiently, and elements in gaseous form emit light when electricity passes through them. This is the source of light emitted by neon signs and is also the source of light in a fire. Figure 9.4.1 : Human/Need/Desire. Neon sculpture by Bruce Nauman (1983), who has been characterized as a conceptual artist. Each Element Has a Unique Spectrum The light frequencies emitted by atoms are mixed together by our eyes so that we see a blended color. Several physicists, including Angstrom in 1868 and Balmer in 1875, passed the light from energized atoms through glass prisms in such a way that the light was spread out so they could see the individual frequencies that made up the light. The emission spectrum (or atomic spectrum) of a chemical element is the unique pattern of light obtained when the element is subjected to heat or electricity. Figure 9.4.2 : Atomic Emission Spectrum of Hydrogen. When hydrogen gas is placed into a tube and electric current passed through it, the color of emitted light is pink. But when the color is spread out, we see that the hydrogen spectrum is composed of four individual frequencies. The pink color of the tube is the result of our eyes blending the four colors. Every atom has its own characteristic spectrum; no two atomic spectra are alike. The image below shows the emission spectrum of iron. Because each element has a unique emission spectrum, elements can be defined using them. Figure 9.4.3 : Atomic Emission Spectrum of Iron. You may have heard or read about scientists discussing what elements are present in the sun or some more distant star, and after hearing that, wondered how scientists could know what elements were present in a place no one has ever been. Scientists determine what elements are present in distant stars by analyzing the light that comes from stars and finding the atomic spectrum of elements in that light. If the exact four lines that compose hydrogen's atomic spectrum are present in the light emitted from the star, that element contains hydrogen. 9.4.1 https://chem.libretexts.org/@go/page/47516 Bohr's Model of the Atom By 1913, the concept of the atom had evolved from Dalton's indivisible spheres idea, to J. J. Thomson's plum pudding model, and then to Rutherford's nuclear atom theory. Rutherford, in addition to carrying out the brilliant experiment that demonstrated the presence of the atomic nucleus, also proposed that the electrons circled the nucleus in a planetary type motion. The solar system or planetary model of the atom was attractive to scientists because it was similar to something with which they were already familiar, namely the solar system. Figure 9.4.3 : Niels Bohr with Albert Einstein at Paul Ehrenfest's home in Leiden (December 1925). Unfortunately, there was a serious flaw in the planetary model. It was already known that when a charged particle (such as an electron) moves in a curved path, it gives off some form of light and loses energy in doing so. This is, after all, how we produce TV signals. If the electron circling the nucleus in an atom loses energy, it would necessarily have to move closer to the nucleus as it loses energy, and would eventually crash into the nucleus. Furthermore, Rutherford's model was unable to describe how electrons give off light forming each element's unique atomic spectrum. These difficulties cast a shadow on the planetary model and indicated that, eventually, it would have to be replaced. In 1913, the Danish physicist Niels Bohr proposed a model of the electron cloud of an atom in which electrons orbit the nucleus and were able to produce atomic spectra. Understanding Bohr's model requires some knowledge of electromagnetic radiation (or light). Energy Levels Bohr's key idea in his model of the atom is that electrons occupy definite orbitals that require the electron to have a specific amount of energy. In order for an electron to be in the electron cloud of an atom, it must be in one of the allowable orbitals and it must have the precise energy required for that orbit. Orbits closer to the nucleus would require smaller amounts of energy for an electron, and orbits farther from the nucleus would require the electron to have a greater amount of energy. The possible orbits are known as energy levels. One of the weaknesses of Bohr's model was that he could not offer a reason why only certain energy levels or orbits were allowed. 9.4.2 https://chem.libretexts.org/@go/page/47516  Figure 9.4.4 : The energy levels of the electrons can be viewed as rungs on a ladder. Note that the spacing between rungs gets smaller at higher energies (CC BY-NC; Ümit Kaya) Bohr hypothesized that the only way electrons could gain or lose energy would be to move from one energy level to another, thus gaining or losing precise amounts of energy. The energy levels are quantized, meaning that only specific amounts are possible. It would be like a ladder that had rungs only at certain heights. The only way you can be on that ladder is to be on one of the rungs, and the only way you could move up or down would be to move to one of the other rungs. Suppose we had such a ladder with 10 rungs. Other rules for the ladder are that only one person can be on a rung in the normal state, and the ladder occupants must be on the lowest rung available. If the ladder had five people on it, they would be on the lowest five rungs. In this situation, no person could move down because all of the lower rungs are full. Bohr worked out rules for the maximum number of electrons that could be in each energy level in his model, and required that an atom in its normal state (ground state) had all electrons in the lowest energy levels available. Under these circumstances, no electron could lose energy because no electron could move down to a lower energy level. In this way, Bohr's model explained why electrons circling the nucleus did not emit energy and spiral into the nucleus. Figure 9.4.5 : In Bohr's Model of the atom, electrons absorb energy to move to a higher level and release energy to move to lower levels. (CC BY-SA 3.0; Kurzon). 9.4.3 https://chem.libretexts.org/@go/page/47516 Bohr's Model and Atomic Spectra The evidence used to support Bohr's model came from the atomic spectra. He suggested that an atomic spectrum is made by the electrons in an atom moving energy levels. The electrons typically have the lowest energy possible, called the ground state. If the electrons are given energy (through heat, electricity, light, etc.) the electrons in an atom could absorb energy by jumping to a higher energy level, or excited state. The electrons then give off the energy in the form of a piece of light—called a photon—that they had absorbed, to fall back to a lower energy level. The energy emitted by electrons dropping back to lower energy levels will always be precise amounts of energy, because the differences in energy levels are precise. This explains why you see specific lines of light when looking at an atomic spectrum—each line of light matches a specific "step down" that an electron can take in that atom. This also explains why each element produces a different atomic spectrum. Because each element has different acceptable energy levels for its electrons, the possible steps each element's electrons can take differ from all other elements. Summary Bohr's model suggests each atom has a set of unchangeable energy levels, and electrons in the electron cloud of that atom must be in one of those energy levels. Bohr's model suggests that the atomic spectra of atoms is produced by electrons gaining energy from some source, jumping up to a higher energy level, then immediately dropping back to a lower energy level and emitting the energy difference between the two energy levels. The existence of the atomic spectra is support for Bohr's model of the atom. Bohr's model was only successful in calculating energy levels for the hydrogen atom. Vocabulary Emission spectrum (or atomic spectrum) - The unique pattern of light given off by an element when it is given energy. Energy levels - Possible orbits that an electron can have in the electron cloud of an atom. Ground state - To be in the lowest energy level possible. Excited state - To be in a higher energy level. Photon - A piece of electromagnetic radiation, or light, with a specific amount of energy. Quantized - To have a specific amount. 9.4: The Bohr Model - Atoms with Orbits is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 9.4.4 https://chem.libretexts.org/@go/page/47516 9.5: The Quantum-Mechanical Model- Atoms with Orbitals  Learning Objectives Define quantum mechanics Differentiate between an orbit and an orbital. How do you study something that seemingly makes no sense? We talk about electrons being in orbits and it sounds like we can tell where that electron is at any moment. We can draw pictures of electrons in orbit, but the reality is that we don't know exactly where they are. We are going to take a look at an area of science that even leaves scientists puzzled. When asked about quantum mechanics, Niels Bohr (who proposed the Bohr model of the atom) said: "Anyone who is not shocked by quantum theory has not understood it". Richard Feynman (one of the founders of modern quantum theory) stated: "I think I can safely say that nobody understands quantum theory." So, let's take a short trip into a land that challenges our everyday world. Quantum Mechanics The study of motion of large objects such as baseballs is called mechanics, or more specifically, classical mechanics. Because of the quantum nature of the electron and other tiny particles moving at high speeds, classical mechanics is inadequate to accurately describe their motion. Quantum mechanics is the study of the motion of objects that are atomic or subatomic in size and thus demonstrate wave-particle duality. In classical mechanics, the size and mass of the objects involved effectively obscures any quantum effects, so that such objects appear to gain or lose energies in any amounts. Particles whose motion is described by quantum mechanics gain or lose energy in small pieces called quanta. One of the fundamental (and hardest to understand) principles of quantum mechanics is that the electron is both a particle and a wave. In the everyday macroscopic world of things we can see, something cannot be both. But this duality can exist in the quantum world of the submicroscopic on the atomic scale. At the heart of quantum mechanics is the idea that we cannot accurately specify the location of an electron. All we can say is that there is a probability that it exists within this certain volume of space. The scientist Erwin Schrödinger developed an equation that deals with these calculations, which we will not pursue at this time. Erwin Schrödinger. Recall that in the Bohr model, the exact path of the electron was restricted to very well-defined circular orbits around the nucleus. An orbital is the quantum mechanical refinement of Bohr’s orbit. In contrast to his concept of a simple circular orbit with a fixed radius, orbitals are mathematically derived regions of space with different probabilities of having an electron. Summary Quantum mechanics involves the study of material at the atomic level. This field deals with probabilities, since we cannot definitely locate a particle. Orbitals are mathematically derived regions of space with different probabilities of having an electron. 9.5: The Quantum-Mechanical Model- Atoms with Orbitals is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 9.5.1 https://chem.libretexts.org/@go/page/47517 9.6: Quantum-Mechanical Orbitals and Electron Configurations  Learning Objectives Represent the organization of electrons by an electron configuration and orbital diagram. The flight path of a commercial airliner is carefully regulated by the Federal Aviation Administration. Each airplane must maintain a distance of five miles from another plane flying at the same altitude and 2,000 feet above and below another aircraft (1,000 feet if the altitude is less than 29,000 feet). So, each aircraft only has certain positions it is allowed to maintain while it flies. As we explore quantum mechanics, we see that electrons have similar restrictions on their locations. Orbitals We can apply our knowledge of quantum numbers to describe the arrangement of electrons for a given atom. We do this with something called electron configurations. They are effectively a map of the electrons for a given atom. We look at the four quantum numbers for a given electron and then assign that electron to a specific orbital below. s Orbitals For any value of n , a value of l = 0 places that electron in an s orbital. This orbital is spherical in shape: Figure 9.6.1 : s orbitals have no orientational preference and resemble spheres. p Orbitals For the table below, we see that we can have three possible orbitals when l = 1. These are designated as p orbitals and have dumbbell shapes. Each of the p orbitals has a different orientation in three-dimensional space. Figure 9.6.2 : p orbitals have an orientational preference and resemble dumbbells. d Orbitals When l = 2 , m values can be l −2, −1, 0, +1, +2 for a total of five d orbitals. Note that all five of the orbitals have specific three-dimensional orientations. Figure 9.6.3 : d orbitals have an orientational preference and exhibit complex structures. f Orbitals The most complex set of orbitals are the f orbitals. When l = 3 , m values can be −3, −2, l −1, 0, +1, +2, +3 for a total of seven different orbital shapes. Again, note the specific orientations of the different f orbitals. 9.6.1 https://chem.libretexts.org/@go/page/47518  Figure 9.6.4 : f orbitals have an orientational preference and exhibit quite complex structures. Orbitals that have the same value of the principal quantum number form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number. Some of the allowed combinations of quantum numbers are compared in Table 9.6.1. Table 9.6.1 : Electron Arrangement Within Energy Levels Number of Orbitals Number of Electrons Principal Quantum Number of Orbitals Number of Electrons Allowable Sublevels per Principal Energy per Principal Energy Number (n) per Sublevel per Sublevel Level Level 1 s 1 1 2 2 s 1 2 2 4 8 p 3 6 s 1 2 3 p 3 9 6 18 d 5 10 s 1 2 p 3 6 4 16 32 d 5 10 f 7 14 Electron Configurations Can you name one thing that easily distinguishes you from the rest of the world? And we're not talking about DNA—that's a little expensive to sequence. For many people, it is their email address. Your email address allows people all over the world to contact you. It does not belong to anyone else, but serves to identify you. Electrons also have a unique set of identifiers in the quantum numbers that describe their location and spin. Chemists use an electronic configuration to represent the organization of electrons in shells and subshells in an atom. An electron configuration simply lists the shell and subshell labels, with a right superscript giving the number of electrons in that subshell. The shells and subshells are listed in the order of filling. Electrons are typically organized around an atom by starting at the lowest possible quantum numbers first, which are the shells-subshells with lower energies. For example, an H atom has a single electron in the 1s subshell. Its electron configuration is 1 H : 1s He has two electrons in the 1s subshell. Its electron configuration is 2 He : 1s The three electrons for Li are arranged in the 1s subshell (two electrons) and the 2s subshell (one electron). The electron configuration of Li is 2 1 Li : 1 s 2 s Be has four electrons, two in the 1s subshell and two in the 2s subshell. Its electron configuration is 2 2 Be : 1 s 2 s 9.6.2 https://chem.libretexts.org/@go/page/47518 Now that the 2s subshell is filled, electrons in larger atoms must go into the 2p subshell, which can hold a maximum of six electrons. The next six elements progressively fill up the 2p subshell: B: 1s22s22p1 C: 1s22s22p2 N: 1s22s22p3 O: 1s22s22p4 F: 1s22s22p5 Ne: 1s22s22p6 Now that the 2p subshell is filled (all possible subshells in the n = 2 shell), the next electron for the next-larger atom must go into the n = 3 shell, s subshell. Second Period Elements Periods refer to the horizontal rows of the periodic table. Looking at a periodic table you will see that the first period contains only the elements hydrogen and helium. This is because the first principal energy level consists of only the s sublevel and so only two electrons are required in order to fill the entire principal energy level. Each time a new principal energy level begins, as with the third element lithium, a new period is started on the periodic table. As one moves across the second period, electrons are successively added. With beryllium (Z = 4) , the 2s sublevel is complete and the 2p sublevel begins with boron (Z = 5). Since there are three 2p orbitals and each orbital holds two electrons, the 2p sublevel is filled after six elements. Table 9.6.1 shows the electron configurations of the elements in the second period. Table 9.6.2 : Electron Configurations of Second-Period Elements Element Name Symbol Atomic Number Electron Configuration Lithium Li 3 1s 2s 2 1 Beryllium Be 4 1s 2s 2 2 Boron B 5 2 1s 2s 2p 2 1 Carbon C 6 2 1s 2s 2p 2 2 Nitrogen N 7 2 1s 2s 2p 2 3 Oxygen O 8 2 1s 2s 2p 2 4 Fluorine F 9 2 1s 2s 2p 2 5 Neon Ne 10 2 1s 2s 2p 2 6 Aufbau Principle Construction of a building begins at the bottom. The foundation is laid and the building goes up step by step. You obviously cannot start with the roof since there is no place to hang it. The building goes from the lowest level to the highest level in a systematic way. In order to create ground state electron configurations for any element, it is necessary to know the way in which the atomic sublevels are organized in order of increasing energy. Figure 9.6.5 shows the order of increasing energy of the sublevels. The lowest energy sublevel is always the 1s sublevel, which consists of one orbital. The single electron of the hydrogen atom will occupy the 1s orbital when the atom is in its ground state. As we proceed with atoms with multiple electrons, those electrons are added to the next lowest sublevel: 2s, 2p, 3s, and so on. The Aufbau principle states that an electron occupies orbitals in order from lowest energy to highest. The Aufbau (German: "building up, construction") principle is sometimes referred to as the "building up" principle. It is worth noting that in reality atoms are not built by adding protons and electrons one at a time, and that this method is merely an aid for us to understand the end result. 9.6.3 https://chem.libretexts.org/@go/page/47518  Figure 9.6.5 : Electrons are added to atomic orbitals in order from low energy (bottom of the graph) to high (top of the graph) according to the Aufbau principle. Principle energy levels are color coded, while sublevels are grouped together and each circle represents an orbital capable of holding two electrons. As seen in the figure above, the energies of the sublevels in different principal energy levels eventually begin to overlap. After the 3p sublevel, it would seem logical that the 3d sublevel should be the next lowest in energy. However, the 4s sublevel is slightly lower in energy than the 3d sublevel and thus fills first. Following the filling of the 3d sublevel is the 4p, then the 5s and the 4d. Note that the 4f sublevel does not fill until just after the 6s sublevel. Figure 9.6.6 is a useful and simple aid for keeping track of the order of fill of the atomic sublevels. Figure 9.6.6 : The arrow leads through each subshell in the appropriate filling order for electron configurations. This chart is straightforward to construct. Simply make a column for all the s orbitals with each n shell on a separate row. Repeat for p, d, and f. Be sure to only include orbitals allowed by the quantum numbers (no 1p or 2d, and so forth). Finally, draw diagonal lines from top to bottom as shown. 9.6.4 https://chem.libretexts.org/@go/page/47518  Energy levels, sublevels, & orbitals Video 9.6.1 : Energy levels, sublevels and orbitals.  Example 9.6.1: Nitrogen Atoms Nitrogen has 7 electrons. Write the electron configuration for nitrogen. Solution: Take a close look at Figure 9.6.5, and use it to figure out how many electrons go into each sublevel, and also the order in which the different sublevels get filled. 1. Begin by filling up the 1s sublevel. This gives 1s2. Now all of the orbitals in the red n = 1 block are filled. Since we used 2 electrons, there are 7 − 2 = 5 electrons left 2. Next, fill the 2s sublevel. This gives 1s22s2. Now all of the orbitals in the s sublevel of the orange n = 2 block are filled. Since we used another 2 electrons, there are 5 − 2 = 3 electrons left 3. Notice that we haven't filled the entire n = 2 block yet… there are still the p orbitals! The final 3 electrons go into the 2p sublevel. This gives 1s22s22p3 The overall electron configuration is: 1s22s22p3.  Example 9.6.2: Potassium Atoms Potassium has 19 electrons. Write the electron configuration code for potassium. Solution This time, take a close look at Figure 9.6.5. 1. Begin by filling up the 1s sublevel. This gives 1s2. Now the n = 1 level is filled. Since we used 2 electrons, there are 19 − 2 = 17 electrons left 2. Next, fill the 2s sublevel. This gives 1s22s2 Since we used another 2 electrons, there are 17 − 2 = 15 electrons left 3. Next, fill the 2p sublevel. This gives 1s22s22p6. Now the n = 2 level is filled. Since we used another 6 electrons, there are 15 − 6 = 9 electrons left 4. Next, fill the 3s sublevel. This gives 1s22s22p63s2 9.6.5 https://chem.libretexts.org/@go/page/47518  Since we used another 2 electrons, there are 9 − 2 = 7 electrons left 5. Next, fill the 3p sublevel. This gives 1s22s22p63s23p6 Since we used another 6 electrons, there are 7 − 6 = 1 electron left Here's where we have to be careful – right after 3p6! Remember, 4s comes before 3d 6. The final electron goes into the 4s sublevel. This gives 1s22s22p63s23p64s1 The overall electron configuration is: 1s22s22p63s23p64s1  Exercise 9.6.1: Magnesium and Sodium Atoms What is the electron configuration for Mg and Na? Answer Mg Mg: 1s22s22p63s2 Answer Na Na: 1s22s22p63s1 Pauli Exclusion Principle When we look at the orbital possibilities for a given atom, we see that there are different arrangements of electrons for each different type of atom. Since each electron must maintain its unique identity, we intuitively sense that the four quantum numbers for any given electron must not match up exactly with the four quantum numbers for any other electron in that atom. For the hydrogen atom, there is no problem since there is only one electron in the H atom. However, when we get to helium we see that the first three quantum numbers for the two electrons are the same: same energy level, same spherical shape. What 1 1 differentiates the two helium electrons is their spin. One of the electrons has a + spin while the other electron has a − spin. So 2 2 the two electrons in the 1s orbital are each unique and distinct from one another because their spins are different. This observation leads to the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers. The energy of the electron is specified by the principal, angular momentum, and magnetic quantum numbers. If those three numbers are identical for two electrons, the spin numbers must be different in order for the two electrons to be differentiated from one another. The two values of the spin quantum number allow each orbital to hold two electrons. Figure 9.6.7 shows how the electrons are indicated in a diagram. Figure 9.6.7 : In an orbital filling diagram, a square represents an orbital, while arrows represent electrons. An arrow pointing upward represents one spin direction, while an arrow pointing downward represents the other spin direction. Hund's Rule The last of the three rules for constructing electron arrangements requires electrons to be placed one at a time in a set of orbitals within the same sublevel. This minimizes the natural repulsive forces that one electron has for another. Hund's rule states that orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron and that each of the single electrons must have the same spin. The figure below shows how a set of three p orbitals is filled with one, two, three, and four electrons. 9.6.6 https://chem.libretexts.org/@go/page/47518  Figure 9.6.8 : The 2p sublevel, for the elements boron (Z = 5), carbon (Z = 6), nitrogen (Z = 7), and oxygen (Z = 8). According to Hund's rule, as electrons are added to a set of orbitals of equal energy, one electron enters each orbital before any orbital receives a second electron. Orbital Filling Diagrams An orbital filling diagram is the more visual way to represent the arrangement of all the electrons in a particular atom. In an orbital filling diagram, the individual orbitals are shown as circles (or squares) and orbitals within a sublevel are drawn next to each other horizontally. Each sublevel is labeled by its principal energy level and sublevel. Electrons are indicated by arrows inside of the circles. An arrow pointing upwards indicates one spin direction, while a downward pointing arrow indicates the other direction. The orbital filling diagrams for hydrogen, helium, and lithium are shown in the figure below. Figure 9.6.9 : Orbital filling diagrams for hydrogen, helium, and lithium. According to the Aufbau process, sublevels and orbitals are filled with electrons in order of increasing energy. Since the s sublevel consists of just one orbital, the second electron simply pairs up with the first electron as in helium. The next element is lithium and necessitates the use of the next available sublevel, the 2s. The filling diagram for carbon is shown in Figure 9.6.10. There are two 2p electrons for carbon and each occupies its own 2p orbital. Figure 9.6.10 : Orbital filling diagram for carbon. Oxygen has four 2p electrons. After each 2p orbital has one electron in it, the fourth electron can be placed in the first 2p orbital with a spin opposite that of the other electron in that orbital. Figure 9.6.11 : Orbital filling diagram for oxygen. If you keep your papers in manila folders, you can pick up a folder and see how much it weighs. If you want to know how many different papers (articles, bank records, or whatever else you keep in a folder), you have to take everything out and count. A computer directory, on the other hand, tells you exactly how much you have in each file. We can get the same information on atoms. If we use an orbital filling diagram, we have to count arrows. When we look at electron configuration data, we simply add up the numbers. 9.6.7 https://chem.libretexts.org/@go/page/47518  Example 9.6.3: Carbon Atoms Draw the orbital filling diagram for carbon and write its electron configuration. Solution Step 1: List the known quantities and plan the problem. Known Atomic number of carbon, Z=6 Use the order of fill diagram to draw an orbital filling diagram with a total of six electrons. Follow Hund's rule. Write the electron configuration. Step 2: Construct the diagram. Orbital filling diagram for carbon. Electron configuration 1s22s22p2 Step 3: Think about your result. Following the 2s sublevel is the 2p, and p sublevels always consist of three orbitals. All three orbitals need to be drawn even if one or more is unoccupied. According to Hund's rule, the sixth electron enters the second of those p orbitals and has the same spin as the fifth electron.  Exercise 9.6.2: Electronic Configurations Write the electron configurations and orbital diagrams for a. Potassium atom: K b. Arsenic atom: As c. Phosphorus atom: P Answer a: Potassium: 1s 2 2 6 2s 2p 3s 3p 4s 2 6 1 Answer b: Arsenic: 1s 2 2 6 2s 2p 3s 3p 4s 3d 2 6 2 10 3 4p Answer c: Phosphorus 1s 2 2 2s 2p 3s 3p 6 2 3 9.6.8 https://chem.libretexts.org/@go/page/47518   The Atom Neighborhood Figure 9.6.12 : The atom neighborhood. Source: Dr. Binh Dao, Sacramento City College. Summary There are four different classes of electron orbitals. These orbitals are determined by the value of the angular momentum quantum number ℓ. An orbital is a wave function for an electron defined by the three quantum numbers, n, ℓ and m ℓ. Orbitals define regions in space where you are likely to find electrons. s orbitals (ℓ = 0) are spherical shaped. p orbitals (ℓ = 1) are dumb-bell shaped. The three possible p orbitals are always perpendicular to each other. Electron configuration notation simplifies the indication of where electrons are located in a specific atom. Superscripts are used to indicate the number of electrons in a given sublevel. The Aufbau principle gives the order of electron filling in an atom. It can be used to describe the locations and energy levels of every electron in a given atom. Hund's rule specifies the order of electron filling within a set of orbitals. Orbital filling diagrams are a way of indicating electron locations in orbitals. The Pauli exclusion principle specifies limits on how identical quantum numbers can be for two electrons in the same atom. Vocabulary principal quantum number (n) Defines the energy level of the wave function for an electron, the size of the electron's standing wave, and the number of nodes in that wave. quantum numbers Integer numbers assigned to certain quantities in the electron wave function. Because electron standing waves must be continuous and must not "double over" on themselves, quantum numbers are restricted to integer values. Contributions & Attributions Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193- [email protected]). 9.6.9 https://chem.libretexts.org/@go/page/47518 9.6: Quantum-Mechanical Orbitals and Electron Configurations is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 9.6.10 https://chem.libretexts.org/@go/page/47518 9.7: Electron Configurations and the Periodic Table  Learning Objectives Relate the electron configurations of the elements to the shape of the periodic table. Determine the expected electron configuration of an element by its place on the periodic table. Previously, we introduced the periodic table as a tool for organizing the known chemical elements. A periodic table is shown in Figure 9.7.1. The elements are listed by atomic number (the number of protons in the nucleus), and elements with similar chemical properties are grouped together in columns. Figure 9.7.1 : The Periodic Table Why does the periodic table have the structure it does? The answer is rather simple, if you understand electron configurations: the shape of the periodic table mimics the filling of the subshells with electrons. The shape of the periodic table mimics the filling of the subshells with electrons. Let us start with H and He. Their electron configurations are 1s1 and 1s2, respectively; with He, the n = 1 shell is filled. These two elements make up the first row of the periodic table (Figure 9.7.2) Figure 9.7.2 : The 1s Subshell. H and He represent the filling of the 1s subshell. The next two electrons, for Li and Be, would go into the 2s subshell. Figure 9.7.3 shows that these two elements are adjacent on the periodic table. 9.7.1 https://chem.libretexts.org/@go/page/47519  Figure 9.7.3 : The 2s Subshell. In Li and Be, the 2s subshell is being filled. For the next six elements, the 2p subshell is being occupied with electrons. On the right side of the periodic table, these six elements (B through Ne) are grouped together (Figure 9.7.4). Figure 9.7.4 : The 2p Subshell. For B through Ne, the 2p subshell is being occupied. The next subshell to be filled is the 3s subshell. The elements when this subshell is being filled, Na and Mg, are back on the left side of the periodic table (Figure 9.7.5). Figure 9.7.5 : The 3s Subshell. Now the 3s subshell is being occupied. Next, the 3p subshell is filled with the next six elements (Figure 9.7.6). 9.7.2 https://chem.libretexts.org/@go/page/47519  Figure 9.7.6 : The 3p Subshell. Next, the 3p subshell is filled with electrons. Instead of filling the 3d subshell next, electrons go into the 4s subshell (Figure 9.7.7). Figure 9.7.7 : The 4s Subshell. The 4s subshell is filled before the 3d subshell. This is reflected in the structure of the periodic table. After the 4s subshell is filled, the 3d subshell is filled with up to 10 electrons. This explains the section of 10 elements in the middle of the periodic table (Figure 9.7.8). Figure 9.7.8 : The 3d Subshell. The 3d subshell is filled in the middle section of the periodic table....And so forth. As we go across the rows of the periodic table, the overall shape of the table outlines how the electrons are occupying the shells and subshells. The first two columns on the left side of the periodic table are where the s subshells are being occupied. Because of this, the first two rows of the periodic table are labeled the s block. Similarly, the p block are the right-most six columns of the periodic table, the d block is the middle 10 columns of the periodic table, while the f block is the 14-column section that is normally depicted as detached from the main body of the periodic table. It could be part of the main body, but then the periodic table would be rather long and cumbersome. Figure 9.7.9 shows the blocks of the periodic table. 9.7.3 https://chem.libretexts.org/@go/page/47519  Figure 9.7.9 : Blocks on the Periodic Table. The periodic table is separated into blocks depending on which subshell is being filled for the atoms that belong in that section. The electrons in the highest-numbered shell, plus any electrons in the last unfilled subshell, are called valence electrons; the highest-numbered shell is called the valence shell. (The inner electrons are called core electrons.) The valence electrons largely control the chemistry of an atom. If we look at just the valence shell’s electron configuration, we find that in each column, the valence shell’s electron configuration is the same. For example, take the elements in the first column of the periodic table: H, Li, Na, K, Rb, and Cs. Their electron configurations (abbreviated for the larger atoms) are as follows, with the valence shell electron configuration highlighted: Electrons, electron configurations, and the valence shell electron configuration highlighted. H: 1s1 Li: 1s22s1 Na: [Ne]3s1 K: [Ar]4s1 Rb: [Kr]5s1 Cs: [Xe]6s1 They all have a similar electron configuration in their valence shells: a single s electron. Because much of the chemistry of an element is influenced by valence electrons, we would expect that these elements would have similar chemistry—and they do. The organization of electrons in atoms explains not only the shape of the periodic table, but also the fact that elements in the same column of the periodic table have similar chemistry. The same concept applies to the other columns of the periodic table. Elements in each column have the same valence shell electron configurations, and the elements have some similar chemical properties. This is strictly true for all elements in the s and p blocks. In the d and f blocks, because there are exceptions to the order of filling of subshells with electrons, similar valence shells are not absolute in these blocks. However, many similarities do exist in these blocks, so a similarity in chemical properties is expected. Similarity of valence shell electron configuration implies that we can determine the electron configuration of an atom solely by its position on the periodic table. Consider Se, as shown in Figure 9.7.10. It is in the fourth column of the p block. This means that its electron configuration should end in a p4 electron configuration. Indeed, the electron configuration of Se is [Ar]4s23d104p4, as expected. 9.7.4 https://chem.libretexts.org/@go/page/47519  Figure 9.7.10 : Selenium on the Periodic Table  Example 9.7.1: Predicting Electron Configurations From the element’s position on the periodic table, predict the valence shell electron configuration for each atom (Figure 9.7.11). Figure 9.7.11 : Various Elements on the Periodic Table a. Ca b. Sn Solution a. Ca is located in the second column of the s block. We expect that its electron configuration should end with s2. Calcium’s electron configuration is [Ar]4s2. b. Sn is located in the second column of the p block, so we expect that its electron configuration would end in p2. Tin’s electron configuration is [Kr]5s24d105p2.  Exercise 9.7.1 From the element’s position on the periodic table, predict the valence shell electron configuration for each atom. Figure 9.7.11. a. Ti b. Cl Answer a [Ar]4s23d2 Answer b [Ne]3s23p5 Summary 9.7.5 https://chem.libretexts.org/@go/page/47519 The arrangement of electrons in atoms is responsible for the shape of the periodic table. Electron configurations can be predicted by the position of an atom on the periodic table. 9.7: Electron Configurations and the Periodic Table is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar- Agnew & Henry Agnew. 9.7.6 https://chem.libretexts.org/@go/page/47519 9.8: The Explanatory Power of the Quantum-Mechanical Model  Learning Objectives Give the name and location of specific groups on the periodic table, including alkali metals, alkaline earth metals, noble gases, halogens, and transition metals. Explain the relationship between the chemical behavior of families in the periodic table and their electron configurations. Identify elements that will have the most similar properties to a given element. The chemical behavior of atoms is controlled by their electron configuration. Since the families of elements were organized by their chemical behavior, it is predictable that the individual members of each chemical family will have similar electron configurations. Families of the Periodic Table Remember that Mendeleev arranged the periodic table so that elements with the most similar properties were placed in the same group. A group is a vertical column of the periodic table. All of the 1A elements have one valence electron. This is what causes these elements to react in the same ways as the other members of the family. The elements in 1A are all very reactive and form compounds in the same ratios with similar properties with other elements. Because of their similarities in their chemical properties, Mendeleev put these elements into the same group. Group 1A is also known as the alkali metals. Although most metals tend to be very hard, these metals are actually soft and can be easily cut. Group 2A is also called the alkaline earth metals. Once again, because of their similarities in electron configurations, these elements have similar properties to each other. The same pattern is true of other groups on the periodic table. Remember, Mendeleev arranged the table so that elements with the most similar properties were in the same group on the periodic table. It is important to recognize a couple of other important groups on the periodic table by their group name. Group 7A (or 17) elements are also called halogens. This group contains very reactive nonmetal elements. The noble gases are in group 8A. These elements also have similar properties to each other, the most significant property being that they are extremely unreactive, rarely forming compounds. The reason for this will be communicated later, when we discuss how compounds form. The elements in this group are also gases at room temperature. An alternate numbering system numbers all of the s , p, and d block elements from 1-18. In this numbering system, group 1A is group 1; group 2A is group 2; the halogens (7A) are group 17; and the noble gases (8A) are group 18. You will come across periodic tables with both numbering systems. It is important to recognize which numbering system is being used, and to be able to find the number of valence electrons in the main block elements, regardless of which numbering system is being used. Periods of the Periodic Table If you can locate an element on the Periodic Table, you can use the element's position to figure out the energy level of the element's valence electrons. A period is a horizontal row of elements on the periodic table. For example, the elements sodium (Na) and magnesium ( Mg ) are both in period 3. The elements astatine (At ) and radon (Rn) are both in period 6. 9.8.1 https://chem.libretexts.org/@go/page/47520 Summary The vertical columns on the periodic table are called groups or families because of their similar chemical behavior. All the members of a family of elements have the same number of valence electrons and similar chemical properties. The horizontal rows on the periodic table are called periods. Vocabulary Group (family) - A vertical column of the periodic table. Alkali metals - Group 1A of the periodic table. Alkaline earth metals - Group 2A of the periodic table. Halogens - Group 7A of the periodic table. Noble gases - Group 8A of the periodic table. Transition elements - Groups 3 to 12 of the periodic table. 9.8: The Explanatory Power of the Quantum-Mechanical Model is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 9.8.2 https://chem.libretexts.org/@go/page/47520 9.9: Periodic Trends - Atomic Size, Ionization Energy, and Metallic Character  Learning Objectives Be able to state how certain properties of atoms vary based on their relative position on the periodic table. One of the reasons the periodic table is so useful is because its structure allows us to qualitatively determine how some properties of the elements vary versus their position on the periodic table. The variations of properties versus positions on the periodic table are called periodic trends. There is no other tool in science that allows us to judge relative properties of a class of objects like this, which makes the periodic table a very useful tool. Many periodic trends are general. There may be a few points where an opposite trend is seen, but there is an overall trend when considered across a whole row or down a whole column of the periodic table. The first periodic trend we will consider is atomic radius. The atomic radius is an indication of the size of an atom. Although the concept of a definite radius of an atom is a bit fuzzy, atoms behave as if they have a certain radius. Such radii can be estimated from various experimental techniques, such as the x-ray crystallography of crystals. As you go down a column of the periodic table, the atomic radii increase. This is because the valence electron shell is getting larger and there is a larger principal quantum number, so the valence shell lies physically farther away from the nucleus. This trend can be summarized as follows: \[as\downarrow PT,atomic\; radius \uparrow \nonumber \] where PT stands for periodic table. Going across a row on the periodic table, left to right, the trend is different. Even though the valence shell maintains the same principal quantum number, the number of protons—and hence the nuclear charge—is increasing as you go across the row. The increasing positive charge casts a tighter grip on the valence electrons, so as you go across the periodic table, the atomic radii decrease. Again, we can summarize this trend as follows: as → P T , atomic radius ↓ Figure 9.9.1 shows spheres representing the atoms of the s and p blocks from the periodic table to scale, showing the two trends for the atomic radius. Figure 9.9.1 : Atomic Radii Trends on the Periodic Table. Although there are some reversals in the trend (e.g., see Po in the bottom row), atoms generally get smaller as you go across the periodic table and larger as you go down any one column. Numbers are the radii in pm. 9.9.1 https://chem.libretexts.org/@go/page/47521   Example 9.9.1: Atomic Radii Referring only to a periodic table and not to Figure 9.9.1, which atom is larger in each pair? a. Si or S b. S or Te Solution a. Si is to the left of S on the periodic table; it is larger because as you go across the row, the atoms get smaller. b. S is above Te on the periodic table; Te is larger because as you go down the column, the atoms get larger.  Exercise 9.9.1: Atomic Radii Referring only to a periodic table and not to Figure 9.9.1, which atom is smaller, Ca or Br? Answer Br Ionization energy (IE) is the amount of energy required to remove an electron from an atom in the gas phase: + − A(g) → A (g) + e ΔH ≡ I E IE is usually expressed in kJ/mol of atoms. It is always positive because the removal of an electron always requires that energy be put in (i.e., it is endothermic). IE also shows periodic trends. As you go down the periodic table, it becomes easier to remove an electron from an atom (i.e., IE decreases) because the valence electron is farther away from the nucleus. Thus, as ↓ P T , I E ↓ However, as you go across the periodic table and the electrons get drawn closer in, it takes more energy to remove an electron; as a result, IE increases: as → P T , I E ↑ Figure 9.9.2 shows values of IE versus position on the periodic table. Again, the trend is not absolute, but the general trends going across and down the periodic table should be obvious. Figure 9.9.2 : Ionization Energy on the Periodic Table. Values are in kJ/mol. 9.9.2 https://chem.libretexts.org/@go/page/47521 IE also shows an interesting trend within a given atom. This is because more than one IE can be defined by removing successive electrons (if the atom has them to begin with): First Ionization Energy (IE1): + − A(g) → A (g) + e Second Ionization Energy (IE2): + 2+ − A (g) → A (g) + e Third Ionization Energy (IE3): 2+ 3+ − A (g) → A (g) + e and so forth. Each successive IE is larger than the previous because an electron is being removed from an atom with a progressively larger positive charge. However, IE takes a large jump when a successive ionization goes down into a new shell. For example, the following are the first three IEs for Mg, whose electron configuration is 1s22s22p63s2: First Ionization Energy (IE1) = 738 kJ/mol: + − M g(g) → M g (g) + e Second Ionization Energy (IE2) = 1,450 kJ/mol: + 2+ − Mg (g) → M g (g) + e Third Ionization Energy (IE3) = 7,734 kJ/mol: 2+ 3+ − Mg (g) → M g (g) + e The second IE is twice the first, which is not a surprise: the first IE involves removing an electron from a neutral atom, while the second one involves removing an electron from a positive ion. The third IE, however, is over five times the previous one. Why is it so much larger? Because the first two electrons are removed from the 3s subshell, but the third electron has to be removed from the n = 2 shell (specifically, the 2p subshell, which is lower in energy than the n = 3 shell). Thus, it takes much more energy than just overcoming a larger ionic charge would suggest. It is trends like this that demonstrate that electrons within atoms are organized in groups.  Example 9.9.2: Ionization Energies Which atom in each pair has the larger first ionization energy? a. Ca or Sr b. K or K+ Solution a. Because Sr is below Ca on the periodic table, it is easier to remove an electron from it; thus, Ca has the higher IE. b. Because K+ has a positive charge, it will be harder to remove another electron from it, so its IE is larger than that of K. Indeed, it will be significantly larger because the next electron in K+ to be removed comes from another shell.  Exercise 9.9.2: Ionization Energies Which atom has the lower ionization energy, C or F? Answer C The opposite of IE is described by electron affinity (EA), which is the energy change when a gas-phase atom accepts an electron: \[A(g)+e^{-}\rightarrow A^{-}(g)\; \; \; \; \; \Delta H\equiv EA \nonumber \] 9.9.3 https://chem.libretexts.org/@go/page/47521 EA is also usually expressed in kJ/mol. EA also demonstrates some periodic trends, although they are less obvious than the other periodic trends discussed previously. Generally, as you go across the periodic table, EA increases its magnitude: as → P T , EA ↑ There is not a definitive trend as you go down the periodic table; sometimes EA increases, sometimes it decreases. Figure 9.9.3 shows EA values versus position on the periodic table for the s- and p-block elements. The trend is not absolute, especially considering the large positive EA values for the second column. However, the general trend going across the periodic table should be obvious. Figure 9.9.3 : Electron Affinity on the Periodic Table. Values are in kJ/mol.  Example 9.9.3: Electron Affinities Predict which atom in each pair will have the highest magnitude of Electron Affinity. a. C or F b. Na or S Solution a. C and F are in the same row on the periodic table, but F is farther to the right. Therefore, F should have the larger magnitude of EA. b. Na and S are in the same row on the periodic table, but S is farther to the right. Therefore, S should have the larger magnitude of EA.  Exercise 9.9.3: Electron Affinities Predict which atom will have the highest magnitude of Electron Affinity: As or Br. Answer Br 9.9.4 https://chem.libretexts.org/@go/page/47521 Metallic Character The metallic character is used to define the chemical properties that metallic elements present. Generally, metals tend to lose electrons to form cations. Nonmetals tend to gain electrons to form anions. They also have a high oxidation potential—therefore they are easily oxidized and are strong reducing agents. Metals also form basic oxides; the more basic the oxide, the higher the metallic character. Figure 9.9.4 : Courtesy of Jessica Thornton (UCD) As you move across the table from left to right, the metallic character decreases, because the elements easily accept electrons to fill their valance shells. Therefore, these elements take on the nonmetallic character of forming anions. As you move up the table, the metallic character decreases, due to the greater pull that the nucleus has on the outer electrons. This greater pull makes it harder for the atoms to lose electrons and form cations.  Uses of the Periodic Properties of Elements 1. Predict greater or smaller atomic size and radial distribution in neutral atoms and ions. 2. Measure and compare ionization energies. 3. Compare electron affinities and electronegativities. Predict redox potential. Compare metallic character with other elements; ability to form cations. Predict reactions that may or may not occur due to the trends. Determine greater cell potential (sum of oxidation and reduction potential) between reactions. Complete chemical reactions according to trends. Summary Certain properties—notably atomic radius, ionization energies, and electron affinities—can be qualitatively understood by the positions of the elements on the periodic table. The major trends are summarized in the figure below. There are three factors that help in the prediction of the trends in the Periodic Table: number of protons in the nucleus, number of shells, and shielding effect. Various periodic trends (CC BY-SA 4.0; Sandbh via Wikipedia) 9.9.5 https://chem.libretexts.org/@go/page/47521 9.9: Periodic Trends - Atomic Size, Ionization Energy, and Metallic Character is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 9.9.6 https://chem.libretexts.org/@go/page/47521 9.E: Electrons in Atoms and the Periodic Table (Exercises) 9.1: Blimps, Balloons, and Models of the Atom 9.2: Light: Electromagnetic Radiation 9.3: The Electromagnetic Spectrum 1. Choose the correct word for the following statement. Blue light has a (longer or shorter) wavelength than red light. 2. Choose the correct word for the following statement. Yellow light has a (higher or lower) frequency than blue light. 3. Choose the correct word for the following statement. Green light has a (larger or smaller) energy than red light. 4. If "light A" has a longer wavelength than "light B", then "light A" has _______________ "light B". (a) a lower frequency than (b) a higher frequency than (c) the same frequency as 5. If "light C" has a shorter wavelength than "light D", then "light C" has _______________ "light D". (a) a larger energy than (b) a smaller energy than (c) the same energy as 6. If "light E" has a higher frequency than "light F", then "light E" has __________________ "light F". (a) a longer wavelength than (b) a shorter wavelength than (c) the same wavelength as 7. If "light G" has a higher frequency than "light H", then "light G" has __________________ "light H". (a) a larger energy than (b) a smaller energy than (c) the same energy as 8. If "light J" has larger energy than "light K", then "light J" has __________________ "light K". (a) a shorter wavelength than (b) a longer wavelength than (c) the same wavelength as 9. Which of the following statements is true? (a) The frequency of green light is higher than the frequency of blue light and the wavelength of green light is longer than the wavelength of blue light. (b) The frequency of green light is higher than the frequency of blue light and the wavelength of green light is shorter than the wavelength of blue light. (c) The frequency of green light is lower than the frequency of blue light and the wavelength of green light is shorter than the wavelength of blue light. (d) The frequency of green light is lower than the frequency of blue light and the wavelength of green light is longer than the wavelength of blue light. (e) The frequency of green light is the same as the frequency of blue light and the wavelength of green light is shorter than the wavelength of blue light. 9.E.1 https://chem.libretexts.org/@go/page/52964 10. As the wavelength of electromagnetic radiation increases: (a) its energy increases. (b) its frequency increases. (c) its speed increases. (d) more than one of the above statements is true. (e) none of the above statements is true. 11. List three examples of electromagnetic waves. 12. Why do white objects appear white? 13. Name the colors present in white light in order of increasing frequency. 14. Why do objects appear black? 9.4: The Bohr Model: Atoms with Orbits 1. Decide whether each of the following statements is true or false: (a) Niels Bohr suggested that the electrons in an atom were restricted to specific orbits and thus could only have certain energies. (b) Bohr's model of the atom can be used to accurately predict the emission spectrum of hydrogen. (c) Bohr's model of the atom can be used to accurately predict the emission spectrum of neon. (d) According to the Bohr model, electrons have more or less energy depending on how far around an orbit they have traveled. 2. According to the Bohr model, electrons in an atom can only have certain, allowable energies. As a result, we say that the energies of these electrons are _______. 3. The Bohr model accurately predicts the emission spectra of atoms with… (a) less than 1 electron. (b) less than 2 electrons. (c) less than 3 electrons. (d) less than 4 electrons. 4. Consider an He+ atom. Like the hydrogen atom, the He+ atom only contains 1 electron, and thus can be described by the Bohr model. Fill in the blanks in the following statements. (a) An electron falling from the n = 2 orbit of He+ to the n = 1 orbit of He+ releases ______ energy than an electron falling from the n = 3 orbit of He+ to the n = 1 orbit of He+. (b) An electron falling from the n = 2 orbit of He+ to the n = 1 orbit of He+ produces light with a ______ wavelength than the light produced by an electron falling from the n = 3 orbit of He+ to the n = 1 orbit of He+. (c) An electron falling from the n = 2 orbit of He+ to the n = 1 orbit of He+ produces light with a ______ frequency than the light produced by an electron falling from the n = 3 orbit of He+ to the n = 1 orbit of He+. 5. According to the Bohr model, higher energy orbits are located (closer to/further from) the atomic nucleus. This makes sense since negative electrons are (attracted to/repelled from) the positive protons in the nucleus, meaning it must take energy to move the electrons (away from/towards) the nucleus of the atom. 6. According to the Bohr model, what is the energy of an electron in the first Bohr orbit of hydrogen? 7. According to the Bohr model, what is the energy of an electron in the tenth Bohr orbit of hydrogen? 8. According to the Bohr model, what is the energy of an electron in the seventh Bohr orbit of hydrogen? 9. If an electron in a hydrogen atom has an energy of −6.06 × 10−20 J, which Bohr orbit is it in? 10. If an electron in a hydrogen atom has an energy of −2.69 × 10−20 J, which Bohr orbit is it in? 11. If an electron falls from the 5th Bohr orbital of hydrogen to the 3rd Bohr orbital of hydrogen, how much energy is released (you can give the energy as a positive number)? 9.E.2 https://chem.libretexts.org/@go/page/52964 12. If an electron falls from the 6th Bohr orbital of hydrogen to the 3rd Bohr orbital of hydrogen, what wavelength of light is emitted? Is this in the visible light range? 9.5: The Quantum-Mechanical Model: Atoms with Orbitals 9.6: Quantum-Mechanical Orbitals and Electron Configurations 1. Match each quantum number with the property that they describe. Match each quantum number with the property that they describe. (a) n i. shape (b) ℓ ii. orientation in space (c) ml iii. number of nodes 2. A point in an electron wave where there is zero electron density is called a _________. 3. Choose the correct word in each of the following statements. (a) The (higher/lower) the value of n, the more nodes there are in the electron standing wave. (b) The (higher/lower) the value of n, the less energy the electron has. (c) The (more/less) energy the electron has, the more nodes there are in its electron standing wave. 4. Fill in the blank. For lower values of n, the electron density is typically found ________ the nucleus of the atom, while for higher values of n, the electron density is typically found __________the nucleus of the atom. 5. Circle all of the statements that make sense: Schrödinger discovered that certain quantities in the electron wave equation had to be integers, because when they weren't, the wave equation described waves which… (a) were discontinuous (b) were too small (c) were too long and narrow (d) were too short and fat (e) "doubled back" on themselves 6. What are the allowed values of ℓ for an electron standing wave with n = 4? 7. How many values of ℓ are possible for an electron standing wave with n = 9? 8. What are the allowed values of ml for an electron standing wave with ℓ = 3? 9. How many different orientations are possible for an electron standing wave with ℓ = 4? 10. What are the allowed values of ml for n = 2? 11. Fill in the blanks. When ℓ = 0, the electron orbital is _________ and when ℓ = 1, the electron orbital is _________ shaped. 12. The n = 1 s orbital has _____ nodes. 13. The n = 2 s orbital has _____ nodes. 14. The n = 2 p orbital has _____ nodes. 15. The n = 1 p orbital has _____ nodes. 16. There are ____ different p orbitals. 17. What energy level (or value of n) has s, p and d orbitals, but no f orbitals? 18. How many different d orbital orientations are there? 19. How many f orbital orientations are there? 20. How many different orbitals are there in the n = 3 energy level? 1. Write the electron configuration for beryllium. Beryllium has 4 electrons. 2. Write the electron configuration for silicon. Silicon has 14 electrons. 3. Write the electron configuration for nitrogen. Nitrogen has 7 electrons. 4. Write the electron configuration for chromium. Chromium has 24 electrons. 5. Write the electron configuration for silver. Silver has 47 electrons. 9.E.3 https://chem.libretexts.org/@go/page/52964 9.7: Electron Configurations and the Periodic Table 1. Use the Periodic Table to determine the energy level of the valence electrons in each of the following elements. (a) B (b) Ga (c) Rb (d) At (e) He 2. Fill in the blanks: (a) B is in the __ level block of the Periodic Table (b) Sr is in the __ level block of the Periodic Table (c) Fe is in the __ level block of the Periodic Table (d) Cs is in the __ level block of the Periodic Table (e) O is in the __ level block of the Periodic Table 3. Use the Periodic Table to determine the energy level and sublevel of the highest energy electrons in each of the following elements: (a) N (b) Ca (c) Rb (d) P (e) In 4. Decide whether each of the following statements is true or false. (a) Li has valence electrons in the n = 1 energy level. (b) Si has valence electrons in the n = 3 energy level. (c) Ga has valence electrons in the n = 3 energy level. (d) Xe has valence electrons in the n = 5 energy level. (e) P has valence electrons in the n = 2 energy level. 5. Match the element to the sublevel block it is found in: Match the element to the sublevel block it is found in: (a) C i. s sublevel block (b) Cs ii. p sublevel block (c) Ce iii. d sublevel block (d) Cr iv. f sublevel block 6. The first row of the Periodic Table has: (a) 1 element (b) 2 elements (c) 3 elements (d) 4 elements (e) 5 elements 9.E.4 https://chem.libretexts.org/@go/page/52964 7. Use the Periodic Table to determine which of the following elements has the highest energy valence electrons. (a) Sr (b) As (c) H (d) At (e) Na 8. Use the Periodic Table to determine which of the following elements has the lowest energy valence electrons. (a) Ga (b) B (c) Cs (d) Bi (e) Cl 9. Which energy level does the first row in the d sublevel block correspond to? 9.8: The Explanatory Power of the Quantum-Mechanical Model 9.9: Periodic Trends: Atomic Size, Ionization Energy, and Metallic Character 1. Why is the atomic size considered to have "no definite boundary"? 2. How is atomic size measured? (a) using a spectrophotomer (b) using a tiny ruler (called a nano ruler) (c) indirectly (d) directly 3. Draw a visual representation of the atomic radii of an iodine molecule. 4. Which of the following would be smaller? (a) In or Ga (b) K or Cs (c) Te or Po 5. Explain in your own words why Iodine is larger than Bromine. 6. What three factors determine the trend of atomic size going down a group? 7. What groups tend to show this trend? 8. Which of the following would have the largest atomic radii? (a) Si (b) C (c) Sn (d) Pb 9. Which of the following would have the smallest atomic radius? (a) 2s2 (b) 4s24p3 (c) 2s22p4 (d) 4s2 9.E.5 https://chem.libretexts.org/@go/page/52964 10. Arrange the following in order of increasing atomic radii: Tl, B, Ga, Al, In. 11. Arrange the following in order of increasing atomic radii: Ge, Sn, C. 12. Which of the following would be larger? (a) Rb or Sn (b) Ca or As 13. Place the following in order of increasing atomic radii: Mg, Cl, S, Na. 14. Describe the atomic size trend for the rows in the Periodic Table. 15. Draw a visual representation of the periodic table describing the trend of atomic size. 16. Which of the following would have the largest atomic radii? (a) Sr (b) Sn (c) Rb (d) In 17. Which of the following would have the smallest atomic radii? (a) K (b) Kr (c) Ga (d) Ge 18. Place the following elements in order of increasing atomic radii: In, Ca, Mg, Sb, Xe. 19. Place the following elements in order of decreasing atomic radii: Al, Ge, Sr, Bi, Cs. 20. Knowing the trend for the rows, what would you predict to be the effect on the atomic radius if an atom were to gain an electron? Use an example in your explanation. 21. Knowing the trend for the rows, what would you predict to be the effect on the atomic radius if the atom were to lose an electron? Use an example in your explanation. Ionization Energy 1. Define ionization energy and show an example ionization equation. 2. Draw a visual representation of the periodic table describing the trend of ionization energy. 3. Which of the following would have the largest ionization energy? (a) Na (b) Al (c) H (d) He 4. Which of the following would have the smallest ionization energy? (a) K (b) P (c) S (d) Ca 5. Place the following elements in order of increasing ionization energy: Na, O, Ca, Ne, K. 6. Place the following elements in order of decreasing ionization energy: N, Si, S, Mg, He. 7. Using experimental data, the first ionization energy for an element was found to be 600 kJ/mol. The second ionization energy for the ion formed was found to be 1,800 kJ/mol. The third ionization energy for the ion formed was found to be 2,700 kJ/mol. The fourth ionization energy for the ion formed was found to be 11,600 kJ/mol. And finally the fifth ionization energy was 9.E.6 https://chem.libretexts.org/@go/page/52964  found to be 15,000 kJ/mol. Write the reactions for the data represented in this question. To which group does this element belong? Explain. 8. Using electron configurations and your understanding of ionization energy, which would you predict would have higher second ionization energy: Na or Mg? 9. Comparing the first ionization energy (IE1) of calcium, Ca, and magnesium, Mg, : (a) Ca has a higher IE1 because its radius is smaller. (b) Mg has a higher IE1 because its radius is smaller. (c) Ca has a higher IE1 because its outer sub-shell is full. (d) Mg has a higher IE1 because its outer sub-shell is full. (e) they have the same IE1 because they have the same number of valence electrons. 10. Comparing the first ionization energy (IE1) of beryllium, Be, and boron, B: (a) Be has a higher IE1 because its radius is smaller. (b) B has a higher IE1 because its radius is smaller. (c) Be has a higher IE1 because its s sub-shell is full. (d) B has a higher IE1 because its s sub-shell is full. (e) They have the same IE1 because B has only one more electron than Be. Electron Affinity 1. Define electron affinity and show an example equation. 2. Choose the element in each pair that has the lower electron affinity: (a) Li or N (b) Na or Cl (c) Ca or K (d) Mg or F 3. Why is the electron affinity for calcium much higher than that of potassium? 4. Draw a visual representation of the periodic table describing the trend of electron affinity. 5. Which of the following would have the largest electron affinity? (a) Se (b) F (c) Ne (d) Br 6. Which of the following would have the smallest electron affinity? (a) Na (b) Ne (c) Al (d) Rb 7. Place the following elements in order of increasing electron affinity: Te, Br, S, K, Ar. 8. Place the following elements in order of decreasing electron affinity: S, Sn, Pb, F, Cs. 9. Describe the trend that would occur for electron affinities for elements in Period 3. Are there any anomalies? Explain. 10. Comparing the electron affinity (EA) of sulfur, S, and phosphorus, P: (a) S has a higher EA because its radius is smaller. (b) P has a higher EA because its radius is smaller. 9.E.7 https://chem.libretexts.org/@go/page/52964  (c) S has a higher EA because its p sub-shell is half full. (d) P has a higher EA because its p sub-shell is half full. (e) they have the same EA because they are next to each other in the Periodic Table. This page titled 9.E: Electrons in Atoms and the Periodic Table (Exercises) is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew via source content that was edited to the style and standards of the LibreTexts platform. 9.E.8 https://chem.libretexts.org/@go/page/52964