Atomic Theory & Physics Concepts PDF

**Based on experiments John Dalton proposed the first modern atomic theory:** - elements consist of atoms, which cannot be created nor destroyed or divided - atoms of the same element have identical size, mass and properties J.J. Thomson (1856-1940) - discovery of the electron through...

**Based on experiments John Dalton proposed the first modern atomic theory:** - elements consist of atoms, which cannot be created nor destroyed or divided - atoms of the same element have identical size, mass and properties J.J. Thomson (1856-1940) - discovery of the electron through experimentation through cathode ray - \"Plum Pudding Model\" or \"Blueberry Muffin Model\" The experiments by JJ Thomson were the first to provide evidence for the existence of the **electron**, a negatively charged subatomic particle. Thomson applied high voltage to a partially evacuated tube with a metal electrode at each end and observed that a ray was produced that started from the negative electrode, or cathode. He also observed that the negative pole of an applied electric field repelled the ray. By measuring the deflection of the beam of electrons in a magnetic field, Thomson was able to determine the charge to mass ratio of an electron using the formula: Thomson also reasoned that atoms must also contain a positive charge. Thomson postulated that an atom consists of a diffuse cloud of positive charge with negatively charged electrons embedded randomly on it. - JJ Thomsons \"Plum Pudding Model\" or \"Blueberry Muffin Model\" **Radioactivity** - The spontaneous disintegration of the nucleus of an atom. Ernest Rutherford - Henry Becquerel & Marie Curie discovered the radioactive elements - Ernest Rutherford began studies of radioactive elements at McGuil University - **Gold Foil Experiment:** Positively charged alpha particles were fired at a sheet of gold foil. Although most of the alpha particles passed through the gold foil, some deflected at various angles and some never passed though the gold foil. - Rutherford discovered the alpha particle and named the beta particle and gamma ray - Rutherford concluded that atoms consist of negatively charged electrons, orbiting a dense, positively charged nucleus. - Isotopes are atoms with the same number of protons but different number of neutrons. Isotopes of the same element has the same atomic number (Z), which is the same \# of protons but different mass number (each nucleus has a different mass number) - When the nuclei of isotopes are unstable, they are radioactive and called [radioisotopes]. - **What are Radioisotopes?** - - Radioisotopes: an isotope with an unstable nucleus; the nucleus decays and emits radioactive gamma rays and/ or subatomic particles. **Light energy** - Light, or light energy, is electromagnetic radiation. - Visible light is the portion of this spectrum that can be seen by the human eye. James Maxwell - classical theory of light Maxwell theorized that light could act on charged particles because it existed as an electromagnetic wave made of magnetic and electrical fields. - According to Maxwell\'s theory, light is an electromagnetic wave composed of continuous wavelengths that form a spectrum. This came to be the classical theory of light **Heinrich Hertz (1887)** - photoelectric effect Hertz was attempting to generate electromagnetic waves using induction coils, and instead discovered the [photoelectric effect,] in which shinning light on a metal surface causes the emissions of electrons from the metal. Hertz reported the photoelectric effect, but did not attempt to explain it. **Photoelectric effect:** electrons are emitted (released) by matter that absorbs energy from shortwave electromagnetic radiation (ex, visible or UV light) Hertz\'s experiments demonstrated that the frequency of the light was more important in determining the energy of the emitted electrons Planck was studying the spectra of the radiant energy emitted by solid bodies (called blackbodies) heated to incandescence (glowing). When a solid is heated to high temperatures, it begins to glow, first red, then white, then blue. The changes in colour and the corresponding light spectra do not depend on the composition of the solid. The intensity of the light of different colours can be measured and plotted on a graph, to produce a curved line (energy curve) Planck\'s experiment showed that the curve reached a peak and then decreased. The position of the peak correlated to the temperature and moved toward higher light frequencies as an object became hotter. - Plank accounted for the unexpected results of his heating experiment by postulating (suggesting) that matter can gain or lose energy, E, only in whole number multiples according to the equation: E = nhf **E **= energy **n **= integer (1,2,3..) **f** = frequency of the radiation. **h **= Planck\'s constant **Planck\'s constant **= 6.63 X 10^-34^ J. s - Planck knew that radiation was emitted as atoms vibrated back and forth (oscillated). - Einstein later brought Planck\'s hypothesis to its logical conclusion- the light emitted by a solid is quantized. **One burst or packet of energy is known as a quantum of energy** Quantum: a unit or packet of energy (plural: quanta) It is important to keep in mind that there are no intermediate quantities of light energy, just like there are no seven and a half cent coins. It was now clear that energy can only occur in discrete quanta and therefore, a system can transfer energy only in whole quanta. - Planck\'s observations revealed that **as the temperature of an object increases, more of the larger quanta and fewer of the smaller quanta of energy are emitted.** - The colour of the light emitted by a hot object depends on the proportion of the quanta of different energies that are emitted. In this way, light energy seems to have properties similar to particles. Albert Einstein (1879-1955) - received a Nobel Prize in 1921 for a paper explaining the photoelectric effect in terms of quantum theory. Einstein suggested that electromagnetic radiation could be viewed as a stream of particles called **photons**. Photon: a unit of light energy Einstein proposed that an electron was emitted from the surface of a metal because a photon collided with the electron. During the collision, the energy of the photon transferred to the electron. Some of the transferred energy caused the electron to break away from the atom, and the rest was converted to kinetic energy. Kinetic energy is a fundamental concept in physics that quantifies the work performed by an object due to its motion. To free an electron from the atom requires the energy from a minimum of one photon. An electron stays in place because of electrostatic forces. If a single electron absorbs a single photon with the right quantity of energy, the electron can escape the metal surface. If a photon does not have enough energy, no electrons can escape the metal, no matter how many photons strike it. The kinetic energy of the ejected electrons depend on the frequency of light used. When the frequency is below a certain level, called the threshold frequency, no electrons are ejected. In conclusion, Einstein explained that electrons will only absorb specific amounts of energy (photons). Electrons must always be located at a defined energy level, not in between. **Quantum Theory** according to quantum theory, electromagnetic energy is NOT continuous; **instead, energy exists as packets or quanta called photons.** What is light? Maxwell developed the classical electromagnetism theory; this theory depicts light as a transverse wave composed of oscillating electric and magnetic fields which are at right angles to each other and perpendicular to the direction the wave moves. -All electromagnetic radiation moves at the [speed of light] 300,000,000 m/s (in a vacuum) \- all waves move at the speed equal to wavelength x frequency **What is Spectronomy?** **Spectronomy** is the scientific study of the spectra (plural of spectrum) in order to determine the properties of the source of the spectra. Light first passes through a sample, and then is dispersed by a prism, or more commonly, a diffraction grating. The dispersed light forms a spectrum. A detector in the instrument then scans the spectrum and calculates the amount of light absorbed or transmitted at each wavelength. Spectrometers and spectraphotometers measure the intensity of light at different wavelengths in similar ways. **The Atomic Spectrum of the Hydrogen Atom** Hydrogen gas, H~2(g)~ is a molecular element. When a high-energy spark is applied to a sample of hydrogen gas, the hydrogen molecules absorb energy, which breaks some of the H-H bonds. The resulting hydrogen atoms are excited; they contain excess energy. The excited hydrogen atoms release this excess energy by emitting (releasing) light of various wavelengths. When this light is passed though a spectroscope, it forms an **emission spectrum.** **Emission Spectrum:** the spectrum (or pattern of bright lines) seen when the electromagnetic radiation of a substance is passed through a spectrometer. Two types of emission spectrum can be produced, depending on the nature of the source. 1) **Continuous Spectrum**: an emission spectrum that contains all the wavelengths in a specific region of the electromagnetic spectrum (example: when white light passes through a prism, a continuous spectrum appears containing all the wavelengths of visible light) 2) **Line Spectrum:** an emission spectrum that contains only particular wavelengths of the element being studied. Line spectrum arises when excited electrons emit energy. **Scientists later revealed that each element has its own unique line spectrum **- the line spectrum of an element is like a fingerprint (uniquely one of a kind) The Unique line spectrum of the hydrogen atom is significant to the atomic theory because it indicates that the electron of the hydrogen atom can exist only at discrete energy levels. **In simpler terms, the energy of the electron in the hydrogen atom is quantized.** The particular wavelengths of light emitted by the electrons of hydrogen atoms are produced by changes in energy. When excited electrons in hydrogen atoms move to a lower energy level, they emit (release) a photon of light. **This is true for all excited electrons in other atoms as well.** **Bohr Model of the Atom** In 1913, Bohr used the emission spectrum of the hydrogen atom to develop a quantum model for the hydrogen atom. Bohr proposed that electrons could move only in specific orbits around the nucleus. He assigned each orbit a specific energy level, and assumed that the energy level of an orbit increased with its distance from the nucleus- When an electron gained more energy (became excited), it could move into an orbit farther away from the nucleus. Envisioning Bohr\'s Model in relation to Line Spectrum of Hydrogen: Imagine a ball sitting on a staircase. Since the ball can only be positioned on a stair, it can only ever be found at specific distances from the ground. Applying Bohr\'s theory to this analogy, the higher up the staircase the ball is, the more potential energy it has. If the ball moves up the staircase (to a higher energy level), it gains more potential energy. If the ball moves down the staircase (to a lower energy level), it loses potential energy. **Transition**: the movement of an electron from one energy level to another energy level [During a transition to a higher energy level,] an electron absorbs a specific quantity of energy, such as when it is struck by a photon. [During a transition to a lower energy level], an electron emits or released a photon of a particular quantity of energy. The lowest possible energy state for an atom is called **ground state** **There are no excited electrons in the ground state.** Bohrs model assumes that each energy level can hold a maximum number of electrons. 2,8,18. Scientist eventually concluded that Bohr\'s model did not fullt describe the structure of an atom. Yet, Bohr\'s model is of great importance because it included the quantization of energy in atoms and paved the way for later theories. [Electrons do not actually orbit the nucleus.] Quantum Mechanics - the quantum (wave) mechanical model describes an electron as a standing wave - The electron can occupy a series of orbitals. Each orbital has a prescribed possible energy value and spatial distribution. - The exact position of the electron and how its moving can never both be known. This is consistent with Heisenberg\'s uncertainty principle, which states that its impossible to know both the position and the speed of a particle simultaneously. - Orbitals are described as probability distributions and depicted as electron density plots. - The two main ideas of the quantum mechanical model of the atom are that electrons can move between orbitals by absorbing or emitting quanta of energy and that the location of electrons is given by a probability distribution. **Quantum Mechanics- orbitals and probability distribution** - Schrödinger and Heisenberg Schrödingers work on quantum mechanics led to his developement of a mathematical equation, called the Schrödinger wave equation, that could be used to located the electron energy levels. While Schrödinger was trying to measure the location and speed of the electron, Heisenberg, postulated the uncertainty principle. *For atomic sized particles or smaller, any attempt to probe them, changes their position, direction of travel or both.* This idea formed **Heisenberg\'s Uncertainty Principle**; it is impossible to simultaneously know the exact position and speed of an electron. The best we can do is to describe the probability of finding an electron in a specific location **What is wave function?** Wave function is the mathematical probability of finding an electron in a certain region of space. Quantum mechanics Quantum mechanics does not describe how an electron moves or even if it moves.** It only tells us the statistical probability of finding an electron in a given location in an atom**. The area or region we are likely to find an electron is an orbital. **electron probability density** Using wave functions, physicists have created a 3-dimensional electron probability density, which is a plot that indicates regions around the nucleus with the greatest probability of finding an electron. The two main ideas of the quantum mechanical model of the atom are that electrons can be in different orbitals by absorbing or emitting quanta of energy, and that the location of electrons is given by a probability distribution. **Schrödingers wave equation is very complex.** It describes the quantized energies of the electron in an atom as well as the functions that determine the probability of finding electrons in various regions in an atom. Solutions to Schrödinger's equation for the hydrogen atom give many wave functions that describe various types of orbitals. **Each of these types of orbitals has a set of four numbers called quantum numbers, which describe various properties of the orbital. **These numbers are like addresses for locating the position of an electron by its city, street, number, and apartment number. In this subsection, you will learn about the four quantum numbers and what each quantum number represents. Quantum numbers **quantum numbers**: numbers that describe the quantum mechanical properties of orbitals; from the solutions to Schrödinger's wave equation **Principal Quantum number (n )** **principal quantum number (n ) (shells) **: the quantum number that describes the size and energy of an atomic orbital - **describes the size and energy of an orbital** - its has whole number values (n = 1,2,3,4,5..) - The spaces between atomic shells are not equal - As n increases, the energy required for an electron to occupy that orbital increases. Each successive orbital is larger. - electrons with higher energy are less tightly bound to the nucleus - **The Principal Quantum Number (n) pt1** - - - Energy levels in an atom are sometimes called shells. Bohr devised this numberingsystem and called the shell number the principal quantum number. The principal quantum number (n) is the quantum number that describes the size and energy of an atomic orbital. It has whole-number values (1, 2, 3, and so on). It is important to note that the spaces between atomic shells are not equal (Figure 1). As n increases, the energy required for an electron to occupy that orbital increases. Each successive orbital is larger, meaning that an electron occupying that orbit spends more time farther from the nucleus. This also means that electrons with higher energy are less tightly bound to the nucleus. - Recall that Bohr took up the challenge of explaining the line spectrum of the hydrogen atom. Bohr's success led other scientists to pursue the investigation of line spectra in detail because there were observations that still required explanation. In 1891, Albert Michelson discovered that the distinct lines in the hydrogen atom's spectrum actually consisted of many smaller lines. These smaller lines were difficult to see and were unexplained for many years. In 1915, a German physicist, Arnold Sommerfeld, studied the hydrogen atom's spectrum in detail. To explain the extra lines, Sommerfeld proposed the secondary quantum number as a way to describe electron energy sublevels, or subshells. - Subshells are part of the primary energy level. If an energy level is described as a staircase, one regular step actually represents a group of several smaller energy step **secondary quantum number (l ) (subshells) :** the quantum number that describes the shape and energy of an atomic orbital, with whole-number values from 0 to n -- 1 for each value of n. - **describes the shape of an orbital (the sublevel within an energy level)** - **it has whole number values from 0 to n-1 for each value of n** Magnetic quantum number - **describes the orientation of the orbital within a sublevel** - **In an orbital, an electron can have an upspin or a downspin.** The magnetic quantum number (ml ) is the quantum number that describes the orientation of an atomic orbital in space relative to the other orbitals in the atom. It has whole-number values between +l and -l, including 0. The value of m~l~ is related to the orientation of an orbital in space relative to the other orbitals in the atom. The number of different values that ml can have equals the number of orbitals that are possible. For example, when l = 1, there are three possible orbitals: +1, 0, and -1 (Table 2). These three types of orbital are all p orbitals, but they differ from each other by their orientation in space. Think about an xyz coordinate system (Figure 3). **The Spin Quantum Number (m~s~)** - **Samuel Goudsmit and George Unlenbeck founded the fourth quantum number** - **The atom has a magnetic property called a magentic moment, when the atom is placed in an external magnetic field. The magnetic moment of an atom has two orientations.** - **The spin of an electron can have one of two values +1/2 or -1/2** The spectral data indicated that the atom has a magnetic property, called a magnetic moment, when the atom is placed in an external magnetic field. The magnetic moment of an atom has two orientations. Since they knew from classical physics that a spinning charge produces a magnetic moment, it seemed reasonable to assume that the electron could have two oppositely directed **"spin states"** (Figure 7). T**he new quantum number related to the spin of an electron, called the electron spin quantum number (m~s~), can have one of two values: +1/2 and -1/2.** **Pauli\'s Exclusion Principle** **Pauli Exclusion Principle** - **\"In a given atom, no two electrons can have the same set of four quantum numbers (n, l, m~l~, and m~s~)\"** In other words, no two electrons in the same atom can be in the same quantum state Since electrons in the same orbital have the same values of n, l, and m~l~, the Pauli exclusion principle implies that they must have different spin quantum numbers, m~s~. Since only two values of m~s~ are allowed, an orbital can hold only two electrons, which must have opposite spins. This principle will have important implications when you apply the quantum mechanical atomic model to account for electron arrangements of the atoms in the periodic table. **Four Quantum numbers in a nutshell** Four quantum numbers, n, l, m~l~, and m~s~, define the electron's position in the atom. The principal quantum number, n, represents the main energy levels, or shells, the electrons can occupy in an atom and has whole-number values 1, 2, 3, \.... The secondary quantum number, l, represents subshells, gives the shape of the orbital, has values 0 to n - 1, and letters spdf. The magnetic quantum number, m~l~, represents the orientations of the subshells and has values -l to +l. The spin quantum number, m~s~, represents electron spin and has a value of either +1/2 or -1/2. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers (n, l, m~l~, m~s~).