CBSE Class 12 Physics NCERT Solutions: Atoms (Chapter 12)

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 12 PDF

This chapter delves into the fundamental structure of atoms, focusing on the historical development and principles of the Bohr model. It explores concepts like atomic number, electron orbits, and the quantization of energy levels. The solutions cover multiple-choice questions that test understanding of the Bohr radius, binding energy calculations, and the limitations of the Bohr model when applied to multi-electron atoms. Key topics include the inverse relationship between atomic radius and atomic number, the concept of a non-inertial frame of reference in atomic physics, and the reasons why the simple Bohr model is insufficient for complex atoms. These detailed solutions are designed to aid students in grasping the core concepts and preparing effectively for their examinations.

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Board	CBSE
Class	Class 12
Subject	Physics Exemplar
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 12

Chapter summary

Chapter 12, Atoms, provides an in-depth look at atomic structure through the lens of Bohr's model. The NCERT Solutions focus on clarifying the postulates of Bohr's theory, including the quantization of angular momentum and energy levels. They address the calculation of atomic radii for ions and the limitations of the model, particularly concerning multi-electron atoms and the concept of reference frames. This chapter's solutions are crucial for understanding the transition from classical to quantum concepts in atomic physics.

Learning outcomes

Understand the Bohr model of the atom and its postulates.
Calculate the radius of an ion in its ground state using Bohr's model.
Explain the concept of binding energy in atomic systems.
Identify the limitations of the Bohr model for multi-electron atoms.
Analyze the significance of reference frames in atomic physics.
Relate angular momentum quantization to atomic structure.

Topics covered

Paper topics

Bohr's Atomic Model
Atomic Number
Bohr Radius
Electron Orbits
Quantization of Energy
Binding Energy
Angular Momentum Quantization
Limitations of Bohr Model
Screening Effect
Inertial and Non-inertial Frames

Important topics

Bohr's Postulates
Calculation of Atomic Radii
Binding Energy Concepts
Limitations of Bohr Model
Application to Hydrogen-like Ions

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Questions and Solutions

Multiple Choice Questions (MCQs) - Question 1

Q. 1 Taking the Bohr radius as $a_0 = 53$ pm, the radius of Li$^{++}$ ion in its ground state, on the basis of Bohr's model, will be about

53 pm
27 pm
18 pm
13 pm

Solution: The Bohr model establishes that the radius of an electron's orbit is inversely proportional to the atomic number ($Z$) of the element. The formula for the radius ($r_n$) of the $n$-th orbit in a hydrogen-like atom is given by $r_n = \frac{n^2 a_0}{Z}$, where $a_0$ is the Bohr radius and $Z$ is the atomic number. For the ground state, $n=1$. Lithium (Li) has an atomic number $Z=3$. Therefore, for the Li$^{++}$ ion in its ground state ($n=1$), the radius will be $r_1 = \frac{1^2 a_0}{3} = \frac{a_0}{3}$. Given that $a_0 = 53$ pm, the radius of Li$^{++}$ is $\frac{53 \text{ pm}}{3} \approx 17.67$ pm. Rounding this to the nearest option, we get approximately 18 pm. Thus, the correct option is (c).

Multiple Choice Questions - Question 2

Q. 2 The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is $B = -\frac{me^4}{8n^2\epsilon_0^2h^2}$ (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be $B = -\frac{Me^4}{8n^2\epsilon^2h^2}$ (M = proton mass). This last expression is not correct, because

n would not be integral
Bohr-quantisation applies only two electron
the frame in which the electron is at rest is not inertial
the motion of the proton would not be in circular orbits, even approximately.

Solution: Bohr's model assumes that the nucleus is stationary and the electron revolves around it. This is a valid approximation because the mass of the nucleus (proton) is much larger than the mass of the electron, making the nucleus's motion negligible. However, if we choose a frame of reference where the electron is at rest, the proton would be revolving around the electron. This frame of reference is non-inertial because it is accelerating along with the proton's circular motion. The fundamental postulates of Bohr's model, including the quantization conditions, are derived based on classical mechanics applied in an inertial frame. Therefore, applying the same formulas in a non-inertial frame leads to incorrect results. Option (c) correctly identifies this issue.

Multiple Choice Questions - Question 3

Q. 3 The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because

of the electrons not being subject to a central force
of the electrons colliding with each other
of screening effects
the force between the nucleus and an electron will no longer be given by Coulomb's law

Solution: The simple Bohr model is based on the assumption that an electron moves in a circular orbit around the nucleus under the influence of the Coulomb's attractive force, which acts as the centripetal force. This force is a central force, meaning it is directed towards the center (the nucleus). In an atom with many electrons, each electron is influenced not only by the nucleus but also by the other electrons. The presence of other electrons shields or screens the nuclear charge, reducing the effective attractive force experienced by a particular electron. This 'screening effect' means the electron is no longer subject solely to a central force from the nucleus, and the simple Bohr model's assumptions break down. While electron-electron interactions exist and can lead to collisions or complex dynamics, the primary reason the Bohr model fails for multi-electron atoms is the screening effect altering the effective central force. Option (c) is the most accurate reason.

Multiple Choice Questions - Question 4

Q. 4 For the ground state, the electron in the H-atom has an angular momentum = h, according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true,

because Bohr model gives incorrect values of angular momentum
because only one of these would have a minimum energy
angular momentum must be in the direction of spin of electron
because electrons go around only in horizontal orbits

Solution: Bohr's second postulate states that the angular momentum ($L$) of an electron in a stable orbit is quantized and is an integral multiple of $\frac{h}{2\pi}$, where $h$ is Planck's constant. Mathematically, $L = n\frac{h}{2\pi}$, where $n = 1, 2, 3, \dots$ is the principal quantum number. The question mentions that the angular momentum is $h$ for the ground state. If we strictly follow the formula, for the ground state ($n=1$), the angular momentum should be $L = 1 \times \frac{h}{2\pi} = \frac{h}{2\pi}$. The statement that the angular momentum is $h$ is therefore not consistent with the standard Bohr model's quantization rule. While angular momentum is a vector, and its orientation can vary, the fundamental issue highlighted here is the magnitude of the angular momentum as stated in the question versus the Bohr model's quantization rule. The Bohr model itself provides quantized values, and stating it as simply '$h$' is an inaccuracy or a misunderstanding of the quantization condition $L = n\frac{h}{2\pi}$. Therefore, the Bohr model, as commonly understood and applied, gives specific quantized values for angular momentum, and the statement in the question implies a deviation from these correct quantized values.

Common mistakes

Incorrectly applying Bohr's model to multi-electron atoms without considering screening effects.
Confusing inertial and non-inertial frames of reference when analyzing atomic motion.
Misinterpreting the relationship between atomic number and atomic radius.
Overlooking the vector nature of angular momentum in advanced contexts.

Revision tips

Review Bohr's postulates carefully, especially the quantization of energy and angular momentum.
Practice calculating atomic radii for different ions using the formula derived from Bohr's model.
Understand why the Bohr model is a simplified model and its limitations for complex atoms.
Pay attention to the reasoning behind why certain frames of reference are not suitable for atomic calculations.

Practice MCQs

Q1. According to Bohr's model, what is the approximate radius of a Li$^{++}$ ion in its ground state, given that the Bohr radius ($ $a_0$ $) is 53 pm?

Q2. When considering the binding energy of a hydrogen atom from the electron's rest frame, why is the formula $ $B = -$ $\frac{Me^4}{8n^2\epsilon_0^2h^2}$ $ incorrect?

Q3. Why can the simple Bohr model not be directly applied to atoms with multiple electrons?

Q4. The Bohr model states that for the ground state of a hydrogen atom, the electron's angular momentum is $h$. Why is this statement problematic in reality?

Frequently asked questions

What is the Bohr radius and how is it used?

The Bohr radius ($a_0$) is the most probable distance between the electron and the nucleus in a hydrogen atom in its ground state. It serves as a fundamental unit of length in atomic physics and is used to calculate the radii of electron orbits in other hydrogen-like ions.

How does the atomic number affect the radius of an ion in Bohr's model?

In Bohr's model, the radius of an electron's orbit is inversely proportional to the atomic number (Z) of the element. This means that as the atomic number increases, the radius of the orbit decreases, assuming the principal quantum number remains the same.

Why is the Bohr model not suitable for atoms with more than one electron?

The simple Bohr model assumes a single electron orbiting a nucleus. In multi-electron atoms, electron-electron interactions and screening effects significantly alter the forces and energy levels, which the basic Bohr model does not account for.

What is the significance of the binding energy in atomic physics?

Binding energy represents the minimum energy required to separate an electron from an atom or a nucleus from an atom. It is a measure of the stability of the atomic system; a more negative binding energy indicates a more stable system.

What is a non-inertial frame of reference in the context of Bohr's model?

A non-inertial frame of reference is one that is accelerating. If one were to consider the electron at rest, the proton would be moving around it, making the electron's frame non-inertial. Bohr's model relies on inertial frames where Newton's laws apply directly.

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