Class 12 Physics

Chapter 12 Solutions — Atoms

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Solutions

Overview

Step-by-step NCERT solutions for Atoms (Chapter 12, CBSE Class 12 Physics) — every question and answer worked out in full, not just the final result. You can also read the Atoms textbook chapter.

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What these solutions cover

All 9 questions in Atoms are solved in the PDF. Here's what's inside, exercise by exercise:

Exercises

1.
Choose the correct alternative from the clues given at the end of the each statement:
- (a) The size of the atom in Thomson's model is .......... the atomic size in Rutherford's model. (much greater than / no different from / much less than.)
- (b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force. (Thomson's model /…
Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?
A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?
The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.
Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10⁻¹¹ m. What are the radii of the n = 2 and n = 3 orbits?
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
In accordance with the Bohr's model, find the quantum number that characterises the earth's revolution around the sun in an orbit of radius 1.5 × 10¹¹ m with orbital speed 3 × 10⁴ m/s. (Mass of earth = 6.0 × 10²⁴ kg.)

Sample

Worked examples

3 questions from Atoms, solved step by step.

Exercises

A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

Given: Energy difference between levels, Delta E = 2.3 eV

Constants: h = 6.63 × 10⁻³⁴ J s, 1 eV = 1.6 × 10⁻¹⁹ J

Converting energy to joules:

Delta E = 2.3 × 1.6 × 10⁻¹⁹ = 3.68 × 10⁻¹⁹ J

Using Bohr's frequency condition: h * nu = Delta E

nu = Delta E / h = (3.68 × 10⁻¹⁹) / (6.63 × 10⁻³⁴)

nu = 5.55 × 10¹⁴ Hz

Answer: 5.55 × 10¹⁴ Hz

Exercises

The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?

Given: Total energy in ground state, E₁ = -13.6 eV

For an electron in a circular orbit under Coulomb attraction, the virial theorem gives:

Kinetic energy K = -E_total

Potential energy U = 2 E_total

(These follow from: K = e²/(8*pi*eps0*r) and U = -e²/(4*pi*eps0*r) = -2K, so E = K + U = K - 2K = -K.)

Kinetic energy: K = -(-13.6) = +13.6 eV

Potential energy: U = 2 × (-13.6) = -27.2 eV

Check: K + U = 13.6 + (-27.2) = -13.6 eV = E₁. Correct.

Answer: Kinetic energy = +13.6 eV; Potential energy = -27.2 eV

Exercises

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

Given: Initial state nᵢ = 1, final state n_f = 4

Constants: h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s, 1 eV = 1.6 × 10⁻¹⁹ J

Energy of nth level: Eₙ = -13.6 / n² eV

E₁ = -13.6 eV

E₄ = -13.6 / 16 = -0.85 eV

Energy of photon absorbed:

Delta E = E₄ - E₁ = -0.85 - (-13.6) = 12.75 eV

Delta E = 12.75 × 1.6 × 10⁻¹⁹ = 2.04 × 10⁻¹⁸ J

Frequency of photon:

nu = Delta E / h = (2.04 × 10⁻¹⁸) / (6.63 × 10⁻³⁴) = 3.08 × 10¹⁵ Hz

Wavelength of photon:

lambda = c / nu = (3 × 10⁸) / (3.08 × 10¹⁵) = 9.74 × 10⁻⁸ m = 97.4 nm

This wavelength lies in the ultraviolet region (Lyman series).

Answer: Wavelength = 9.74 × 10⁻⁸ m (97.4 nm, UV); Frequency = 3.08 × 10¹⁵ Hz

All 9 questions in Atoms are solved step by step in the Solutions PDF above.

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Chapter 12 Solutions — Atoms

Overview

What these solutions cover

Exercises

Worked examples

A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

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