Structure of the Atom — NCERT Solutions

The properties of the three sub-atomic particles are compared below:

Key points:

• Electrons are negatively charged and revolve around the nucleus in fixed shells.
• Protons are positively charged and are present in the nucleus.
• Neutrons are neutral (no charge) and are also present in the nucleus.
• The mass of an electron is negligible compared to protons and neutrons.

J.J. Thomson's Model (Plum Pudding Model): Thomson proposed that an atom is a sphere of positive charge with electrons embedded in it like plums in a pudding.

Limitations:

1. Thomson's model could not explain the results of Rutherford's alpha-particle scattering experiment. If the positive charge were spread uniformly throughout the atom, the alpha particles should have passed through with very little deflection. However, Rutherford observed that some alpha particles were deflected at large angles and some even bounced back, which Thomson's model could not account for.
2. The model did not mention the existence of a nucleus — a dense, positively charged centre of the atom.
3. It could not explain the stability of the atom in terms of arrangement of electrons.

Conclusion: Thomson's model was an early attempt but was soon replaced by Rutherford's nuclear model.

Rutherford's Nuclear Model: Rutherford proposed that the atom has a tiny, dense, positively charged nucleus at the centre, and electrons revolve around it in circular orbits.

Limitations:

1. Instability of the atom: According to classical electromagnetic theory, a charged particle (electron) moving in a circular orbit continuously loses energy by emitting radiation. As it loses energy, it should spiral inward and eventually fall into the nucleus. This would make the atom unstable and collapse within $10^{-8}$ seconds. But atoms are known to be stable — this contradiction could not be explained by Rutherford's model.
2. Could not explain the atomic spectrum: If electrons lose energy continuously, they should emit a continuous spectrum of radiation. However, atoms emit a line spectrum (discrete lines), which Rutherford's model failed to explain.
3. No information about electronic arrangement: The model did not say anything about how electrons are arranged or distributed around the nucleus.

Conclusion: Rutherford's model was an improvement over Thomson's model but had serious drawbacks that were later addressed by Bohr's model.

Bohr's Model of the Atom (1913):

Neils Bohr proposed an improved model of the atom to overcome the limitations of Rutherford's model. The main postulates are:

1. Nucleus: The atom has a small, dense, positively charged nucleus at its centre (retained from Rutherford's model).

2. Fixed orbits (shells): Electrons revolve around the nucleus in fixed circular paths called orbits or shells. These shells are designated as K, L, M, N, ... (or numbered 1, 2, 3, 4, ...).

3. Discrete energy levels: Each orbit has a fixed amount of energy associated with it. As long as an electron remains in a particular orbit, it does not radiate energy. Hence the atom is stable.

4. Energy change during transition: When an electron jumps from a lower energy orbit to a higher energy orbit, it absorbs energy. When it falls from a higher to a lower orbit, it emits energy in the form of radiation. This explains the line spectrum of atoms.

Diagram (description): The nucleus is at the centre; K shell is closest (lowest energy), followed by L, M, N shells at increasing distances and energies.

Significance: Bohr's model successfully explained the stability of the atom and the line spectrum of hydrogen.

The three atomic models discussed in the chapter are compared below:

Conclusion: Each model was an improvement over the previous one. Bohr's model was the most successful among the three in explaining atomic stability and hydrogen spectrum.

Rules for Distribution of Electrons in Shells (Bohr-Bury Rules):

1. Maximum electrons in a shell: The maximum number of electrons that can be accommodated in a shell is given by the formula $2n^2$, where $n$ is the shell number.

• K shell ($n=1$): $2 \times 1^2 = 2$ electrons
• L shell ($n=2$): $2 \times 2^2 = 8$ electrons
• M shell ($n=3$): $2 \times 3^2 = 18$ electrons (but for first 18 elements, max 8 are filled)

2. Outermost shell rule: The outermost shell cannot have more than 8 electrons, even if the formula allows more.

3. Penultimate shell rule: The second last (penultimate) shell cannot have more than 18 electrons.

4. Sequential filling: Shells are filled in order — a new shell is started only when the inner shell is completely filled.

5. Valence shell: The last shell (outermost) is called the valence shell and the electrons in it are called valence electrons.

Example — Electronic configurations of first 18 elements:

Definition of Valency:
Valency is the combining capacity of an atom of an element. It is determined by the number of electrons in the outermost shell (valence electrons) of an atom.

• If the number of valence electrons is 4 or less, the valency = number of valence electrons.
• If the number of valence electrons is more than 4, the valency = $8 -$ (number of valence electrons).

Example 1 — Silicon (Si):

• Atomic number of Si = 14
• Electronic configuration: K = 2, L = 8, M = 4
• Valence electrons = 4
• Since valence electrons $\leq 4$, Valency of Si = 4
• Silicon can form 4 bonds (e.g., $\text{SiCl}_4$).

Example 2 — Oxygen (O):

• Atomic number of O = 8
• Electronic configuration: K = 2, L = 6
• Valence electrons = 6
• Since valence electrons $> 4$, Valency of O = $8 - 6 =$ 2
• Oxygen can form 2 bonds (e.g., $\text{H}_2\text{O}$).

Conclusion: Valency tells us how many bonds an atom can form with other atoms.

(i) Atomic Number (Z):
The atomic number of an element is defined as the number of protons present in the nucleus of its atom. Since an atom is electrically neutral, the number of protons equals the number of electrons.
$$Z = \text{Number of protons} = \text{Number of electrons}$$
Example: Carbon (C) has 6 protons, so its atomic number $Z = 6$.

(ii) Mass Number (A):
The mass number of an atom is defined as the total number of protons and neutrons (nucleons) present in the nucleus.
$$A = \text{Number of protons} + \text{Number of neutrons}$$
Example: Carbon has 6 protons and 6 neutrons, so its mass number $A = 6 + 6 = 12$. It is written as $^{12}_6\text{C}$.

(iii) Isotopes:
Isotopes are atoms of the same element that have the same atomic number but different mass numbers (i.e., same number of protons but different number of neutrons).
Example: Hydrogen has three isotopes:

• Protium: $^1_1\text{H}$ (1 proton, 0 neutrons)
• Deuterium: $^2_1\text{H}$ (1 proton, 1 neutron)
• Tritium: $^3_1\text{H}$ (1 proton, 2 neutrons)

All have the same atomic number (1) but different mass numbers.

(iv) Isobars:
Isobars are atoms of different elements that have the same mass number but different atomic numbers.
Example: Calcium ($^{40}_{20}\text{Ca}$) and Argon ($^{40}_{18}\text{Ar}$) are isobars — both have mass number 40 but different atomic numbers (20 and 18 respectively).

Two Uses of Isotopes:

1. An isotope of uranium ($^{235}\text{U}$) is used as fuel in nuclear reactors to generate electricity.
2. An isotope of iodine ($^{131}\text{I}$) is used in the treatment of thyroid cancer (goitre).
3. (Bonus) An isotope of cobalt ($^{60}\text{Co}$) is used in the treatment of cancer (radiotherapy).

Given: $\text{Na}^+$ ion has completely filled K and L shells.

Step 1: Electronic configuration of Na atom

• Atomic number of Na = 11
• Number of electrons in Na = 11
• Electronic configuration: K = 2, L = 8, M = 1

Step 2: Formation of Na⁺ ion

• $\text{Na}^+$ is formed when a sodium atom loses 1 electron from its outermost shell (M shell).

$$\text{Na} \rightarrow \text{Na}^+ + e^-$$

• Number of electrons in $\text{Na}^+$ = $11 - 1 = 10$

Step 3: Electronic configuration of Na⁺

• 10 electrons are distributed as: K = 2, L = 8
• K shell capacity = 2 (completely filled ✓)
• L shell capacity = 8 (completely filled ✓)
• M shell has 0 electrons.

Conclusion: Since $\text{Na}^+$ has only 10 electrons, they completely fill the K shell (2 electrons) and L shell (8 electrons), with no electrons in the M shell. Hence, $\text{Na}^+$ has completely filled K and L shells.

Given:

• Isotope 1: $^{79}\text{Br}$, abundance = 49.7%
• Isotope 2: $^{81}\text{Br}$, abundance = 50.3%

Formula:
$$\text{Average atomic mass} = \frac{(\text{mass of isotope 1} \times \% \text{ abundance}_1) + (\text{mass of isotope 2} \times \% \text{ abundance}_2)}{100}$$

Calculation:
$$\text{Average atomic mass} = \frac{(79 \times 49.7) + (81 \times 50.3)}{100}$$

$$= \frac{3926.3 + 4074.3}{100}$$

$$= \frac{8000.6}{100}$$

$$= 80.006 \text{ u}$$

$$\boxed{\text{Average atomic mass of Bromine} \approx 80 \text{ u}}$$