Science Chapter 5: Structure of Matter PDF

Science Chapter Structure of Matter 5 In this chapter, the following topics are discussed: 5 Particles of an Atom, Rutherford's Atomic Model, Bohr's Atomic Model 5 Arrangement of Electrons in the Energy Levels of Atom...

Science Chapter Structure of Matter 5 In this chapter, the following topics are discussed: 5 Particles of an Atom, Rutherford's Atomic Model, Bohr's Atomic Model 5 Arrangement of Electrons in the Energy Levels of Atom 5 Atomic Mass or Relative Atomic Mass 5 Determining the Relative Atomic Mass of a Molecule from the Isotopic Abundance Percentage 5 Determining the Relative Molecular Mass from the Relative Atomic Mass of an Element 5.1 Particles of an Atom In the previous class, you've learned about the structure of an atom. You know that atoms are primarily composed of three particles: electrons, protons, and neutrons. In the center of the atom is the nucleus, which contains protons and neutrons. Electrons orbit the nucleus, revolving around it. Following are some information about electrons, protons, and neutrons: Electron An electron is a fundamental particle of an atom with a negative charge. Its charge is -1.602 × 10-19 coulombs. J. J. Thomson is credited with the discovery of the electron, as he accurately determined its mass and charge for the first time. Below are some additional characteristics of electrons: 1. The mass of an electron is 9.109 × 10-31 kg, which is approximately 1837 times less than the mass of a proton. Therefore, neglecting the relative mass of electrons compared to neutrons and protons does not result in significant loss or error. Academic year 2024 2. 2. Electrons are assigned a relative charge of -1. Electrons are often denoted by the symbol 'e'. 78  Structure of Matter Proton A proton is a positively charged fundamental particle of an atom. It carries a charge equal to +1.602 × 10-19 coulombs. The discovery of the proton is credited to Ernest Rutherford. Here are some additional characteristics of protons: 1. The mass of a proton is 1.673 × 10-27 kg. 2. Protons can be obtained through the emission of the single electron from a hydrogen atom. 3. Protons have a relative charge of +1 and a relative mass of +1. They are commonly denoted by the symbol 'p'. Neutron James Chadwick discovered the neutron in 1932. Neutrons have no charge and are present in the nucleus of all atoms except hydrogen. Here are some additional important points about neutrons: 1. The difference in the number of neutrons in the nuclei of two different isotopes of an element contributes to the difference in their masses. 2. The mass of a neutron is approximately 1.675 × 10-27 kg, slightly greater than the mass of a proton. 3. Neutrons have a relative charge of 0 and a relative mass of 1. They are commonly denoted by the symbol 'n'. 4. Neutrons exhibit a unique property. When they are inside the nucleus, they are stable, but when they are in a free state, they are unstable. In about 10 minutes, a free neutron undergoes a process called beta decay, splitting into a proton, an electron, and an electron antineutrino. Academic year 2024 5.2 Atomic Model In your previous classes, you have studied the origin and development of the atomic model. The first genuine explanation of atomic structure came after the formulation of 79  Science quantum mechanics. Although quantum mechanics has led to a major breakthrough in science, providing a true explanation of the atomic structure, it didn't happen overnight. It is the result of the combined efforts of numerous scientists, and the understanding has gradually developed through continuous endeavors. Two distinct attempts to explain the structure of the atom can be highlighted—the Rutherford atomic model and the Bohr atomic model. 5.2.1 Rutherford’s Atomic Model Scientists knew that there were oppositely charged particles— electrons and protons— within an atom, but they didn't know how they were arranged. British scientist Ernest Rutherford shed light on this matter for the first time and put forward a model based on his Orbit of electron experimental data. This model Nucleus is known as Rutherford's atomic model (Figure 5.1). The model is Proton as follows: Neutron 1. A positive charge is Electron concentrated at the center of an atom, called the nucleus, where most of the atom's mass is located. Figure 5.1 : Rutherford’s Atomic Model Inside the nucleus, there are protons, and outside the nucleus, there are electrons. Since the mass of an electron is extremely small in comparison, the combined mass of protons and neutrons within the nucleus is considered as the atom's mass. 2. The nucleus is extremely small, and most of the atom's volume is empty. 3. Rutherford proposed in his atomic model that due to the attractive force of the positive charge at the center, negatively charged electrons revolve around it. He compared the motion of electrons centered around the nucleus to the way planets orbit Academic year 2024 the sun in our solar system. In other words, electrons revolve the central nucleus along various orbits. Due to the analogy with the solar system, Rutherford's atomic model is also called 80  Structure of Matter the solar system model or the solar model. Moreover, through this model, Rutherford initiated the concept of the nucleus for the first time, which is why it is also referred to as the nuclear model. Limitations of Rutherford’s Atomic Model: Although the assumption of an extremely small nucleus at the center of the atom was a significant step in Nucleus understanding the structure of the atom, it could not fully explain the Electron atomic structure. Until then, quantum mechanics had not developed enough to explain the stability of the atom according to Rutherford's model. In this model, it is assumed that electrons revolve around the nucleus, but it fails to explain the stability of electrons Figure 5.2 : Electrons lose energy and fall according to Maxwell's theory. According to Maxwell's theory, towards the nucleus electrons, while revolving around the nucleus, continuously lose energy gradually. As a result, the orbit of electrons becomes smaller, and eventually, they fall into the nucleus (Figure 5.2). From this, it is understood that this model does not explain the stability of the atom. Additionally, this model does not provide any information about the radius, shape, or arrangement of electrons in the electron's orbit. Academic year 2024 81  Science 5.2.2 Bohr’s Model In 1913, scientist Niels Bohr addressed the limitations of Rutherford's atomic model and Positively proposed a new atomic model. charged At that time, scientists began to nucleus explore the fundamental concepts of quantum mechanics, and these concepts were applied in developing this model. The main Figure 5.3 : Bohr's Atomic Model: features of Bohr's atomic model The shells K, L, M, N are depicted are: 1. Electrons within an atom do not revolve around the nucleus in any arbitrary orbit. Instead, they only revolve in specific permitted circular orbits of fixed radii. While staying in their stable orbits, electrons do not emit or absorb energy. 2. These stable orbits are represented by the number 'n,' where the values of n are 1, 2, 3, 4, … and so on. These orbits are also referred to as K, L, M, N shells (Figure 5.3). These are also termed as energy levels or shells. Note that when the value of n is lower, it is referred to as a lower energy level, and when the value of n is n=2 n=2 Energy level n=1 n=1 Energy emission Positively charged nucleus Academic year 2024 Energy absorption Figure 5.4 : Bohr's Atomic Model. The principal energy level (n), demonstration of energy absorption or emission when an electron transitions from one energy level to another 82  Structure of Matter higher, it is called a higher energy level. 3. When an electron revolves in its principal energy level, it neither loses nor gains energy. If energy is supplied externally, the absorbed energy makes the electron move from a lower energy level to a higher one (Figure 5.4). Conversely, if an electron moves from a higher energy level to a lower one, energy is emitted. The amount of absorbed or emitted energy (∆E) during the transition between two energy levels (E1, E2) is determined by Planck's equation: ΔE = E2 - E1 = hν Here, ΔE is the absorbed or emitted energy, ℎ is Planck's constant (6.626 ×10-34 m2kg/s), and ν is the frequency of the absorbed or emitted electromagnetic radiation. Bohr's model successfully explained the spectral lines produced by hydrogen (H) atoms using this absorbed energy. Limitations of Bohr’s Atomic Model Despite the remarkable success of Bohr's atomic model, it too had some limitations. While it successfully explained the atomic spectrum of an atom with single-electron, it faced challenges in explaining the spectral lines of multi-electron atoms. According to Bohr's atomic model, when an electron transitions from one energy level to another, a specific amount of energy causes the appearance of a single line in the atomic spectrum. However, upon closer examination, it was observed that each line is, in fact, a collection of numerous closely spaced lines, indicating the presence of various energy levels between the two main levels. 5.3 Electronic Configuration of Atoms Rutherford and Bohr's model, along with the collective efforts of numerous scientists, gradually unveiled the mysteries of atomic structure and how electrons are arranged in atoms. As mentioned earlier, to fully comprehend this fascinating world, one needs to delve into the realm of quantum mechanics. Those of you pursuing advanced studies in physics will have the opportunity to explore the subject comprehensively and Academic year 2024 holistically. However, even without delving into the details of how these rules came about, you can understand the basics of how electrons are organized in an atom by simply applying these rules. You've already gained some insights into the rules governing electron configuration 83  Science in the previous classes. You know that according to Bohr's atomic model, the energy levels of electrons in an atom are referred to as principal energy levels, denoted by the symbol ‘n’. Each principal energy level has a maximum electron-holding capacity given by the formula 2n2, where n = 1, 2, 3, 4, … etc., representing the number of the energy level. The corresponding energy levels are often denoted as K, L, M, N, and so forth, also known as shells. For example, when n = 1, 2n2 = 2 × (1)2 = 2, meaning the first energy level or shell (K shell) can accommodate a maximum of 2 electrons. Similarly, when n = 2, 2n2 = 2 × (2)2 = 8, indicating that the second energy level or shell (L shell) can hold a maximum of 8 electrons. By applying this pattern, you can determine the maximum electron capacity for the subsequent energy levels or shells. To further understand and practice these rules, let's explore the electron configurations of some molecules in the table below. Table: Electron Configuration of Atoms n=1 n=2 n=3 n=4 Atomic K L M N Element Number Maximum Maximum Maximum Maximum 2 Electrons 4 Electrons 18 Electrons 32 Electrons 1 H 1 2 He 2 3 Li 2 1 11 Na 2 8 1 18 Ar 2 8 8 19 K 2 8 8 1 20 Ca 2 8 8 2 21 Sc 2 8 9 2 22 Ti 2 8 10 2 23 V 2 8 11 2 24 Cr 2 8 13 1 Academic year 2024 25 Mn 2 8 13 2 26 Fe 2 8 14 2 30 Zn 2 8 18 2 84  Structure of Matter In the above table, you can see that the atomic number of Hydrogen (H) is 1, indicating that it has 1 electron. Therefore, this electron is entering the first energy level or the K shell. Similarly, according to the rules of electron configuration in atoms, for Lithium (Li) with an atomic number of 3, it has 2 electrons in the first energy level or K shell. Following the electron configuration rules, since the first energy level (K shell) cannot accommodate more than 2 electrons, the third electron enters the second energy level or L shell. In the case of Sodium (Na), the rules dictate that the first energy level (K shell) holds 2 electrons, the second energy level (L shell) holds 8 electrons, and the third energy level (M shell) holds 1 electron. For all the examples in the table, the electron configurations in atoms follow the 2n2 rule. In other words, the number of electrons in an energy level does not exceed 2n2. However, in some cases, the lower energy level is not completely filled, and electrons start to enetr the next higher energy level. For instance, we can see from the table, Potassium (K) and Calcium (Ca) have atomic numbers 19 and 20, respectively, and both have the maximum electron-holding capacity of 18 in the third energy level (M shell). However, the 19th electron of Potassium and the 19th and 20th electrons of Calcium start populating the fourth energy level (N shell) without completely filling the third energy level (M shell). To understand why electrons sometimes leave lower energy levels incomplete and move to higher energy levels, we need to explore a new concept, which is the sub- energy level of electrons. 5.4 Concept of Orbital We know that the principal energy levels are represented by n. These energy levels are further divided into sublevels, denoted by the English letter l. Here, the value of l ranges from 0to n-1. Sublevels are referred to as orbitals. Besides the numerical designations (0, 1, 2, 3...), these orbitals also have distinct names: s, p, d, and f. Now, let's explore the concept of sublevels (l) and orbitals based on the value of the principal energy level (n): When n = 1, there can be only one value for l, which is n – 1 = (1 - 1) = 0. In this case, there will be one orbital, and it will be represented as 1s. Academic year 2024 For n = 2, the maximum value for l is n – 1 = (2 - 1) = 1. Therefore, there can be two values for l: l = 0 and l = 1. This means there will be two orbitals, namely 2s and 2p. 85  Science When n = 3, the maximum value for l is n – 1 = (3 - 1) = 2. Thus, there can be three values for l: l = 0, 1, and 2. This leads to three orbitals: 3s, 3p, and 3d. We can observe a similar pattern for n = 4, where l can be 0, 1, 2, or 3, resulting in four orbitals: 4s, 4p, 4d, and 4f. For n = 5, there will be five orbitals. However, since the first four orbitals (5s, 5p, 5d, and 5f) can accommodate all the electrons, there is no need for additional fifth or other orbitals after the fourth orbital. This holds true for n = 6, 7, and 8 as well. We have divided each principal energy level into its sublevels or orbitals. Now, we need to determine how many electrons can be accommodated in each sublevel or orbital. The way its determined can be properly demonstrated by solving the equations of quantum mechanics, but here we will only mention the results. The number of electrons in an orbital is given by the formula 2(2l + 1). In other words, For l = 0, the maximum number of electrons in s orbital of any n is 2(2 × 0 + 1) = 2. For l = 1, the maximum number of electrons in p orbital of any n is 2(2 × 1 + 1) = 6. For l = 2, the maximum number of electrons in d orbital of any n is 2(2 × 2 + 1) = 10. For l = 3, the maximum number of electrons in f orbital of any n is 2(2 × 3 + 1) = 14. Now, you can easily see that for any n, the total number of electrons found by the sum of electrons in all orbitals follows the 2n2 rule! ୗ Food for Thought: Can you mathematically demonstrate that for any given value of n, the sum of Academic year 2024 electrons in all orbitals is 2n2. In other words, is ? 86  Structure of Matter The table below illustrates the main energy levels (n = 1 to 4), the possible sublevels for each energy level, the names of the orbitals in the respective sublevels, the total number of electrons in each orbital, and the total electron count in the main energy level: Total Main Number of Total Number of Value of Name of Symbol of Electrons in Main Energy Electrons Sublevel l Orbital Orbital Energy Level 2n2 Level (n) in Orbital 2(2l+1) 1 0 s 1s 2 2 0 s 2s 2 2 2+6=8 1 p 2p 6 0 s 3s 2 3 1 p 3p 6 2 + 6 + 10 = 18 2 d 3d 10 0 s 4s 2 1 p 4p 6 2 + 6 + 10 + 14 4 2 d 4d 10 = 32 3 f 4f 14 5.5 Principles of Electron Configuration in Atoms The principles of electron configuration in atoms are described below: 1. According to the electron configuration principles in atoms, electrons fill the orbitals starting from the lowest energy level, and then proceed to fill higher energy level orbitals in sequence. In simpler terms, electrons enter orbitals with Academic year 2024 lowest energy level first, and then gradually enter the higher energy level orbitals. Now, the question arises: How can we determine which orbital has higher or lower energy? To understand this, we need to calculate and compare the sum of the value 87  Science of principal energy level (n) Electron enters and the sublevel (l) for two from this orbital orbitals. The orbital with a lower value of (n + l) has lower energy, and the one with a higher value has higher energy. For example, let's compare the energies of the 3d and 4s orbitals: 3d: (n + l) = (3 + 2) = 5 4s: (n + l) = (4 + 0) = 4 Here, we observe that the 4s orbital in the fourth energy level has lower energy than the 3d orbital in the third energy level. Therefore, following the principles stated above, electrons will first enter the 4s orbital and then go into the Figure 5.5 : Filling Order of Atomic Orbitals 3d orbital. 2. If the values of (n + l) are equal for two orbitals, the orbital with a lower principal energy level (n) has lower energy, and electrons will enter that orbital first. For instance, consider the comparison between the 3d and 4p orbitals: 3d: (n + l) = (3 + 2) = 5 4p: (n + l) = (4 + 1) = 5 Academic year 2024 In this case, both orbitals have the same (n + l) value of 5, but since the value of n for the 3d orbital is 3, and for the 4p orbital is 4, the 3d orbital has lower energy. Consequently, electrons will enter the 3d orbital before the 4p orbital. 88  Structure of Matter By applying these two simple rules, we can arrange all orbitals in order of increasing energy levels: 1s