Atoms — Class 12 Physics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 12 Physics chapter "Atoms" — 6 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 12 Physics chapter "Atoms" — 6 important questions with detailed answers for CBSE board exam preparation.

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

Explain Bohr's model of hydrogen atom. Derive expression for energy levels an…
An electron in hydrogen atom transitions from n = 3 to n = 1. Find the energy…
What are X-rays? Explain characteristic and continuous X-ray spectra.
What is the Franck-Hertz experiment? Explain how it validates Bohr's energy l…
Explain spectral series in hydrogen atom. Write the formula and find the wave…
What is the difference between emission and absorption spectra? Explain conti…

Solutions Summary:

Question	Status
Explain Bohr's model of hydrogen atom. Derive expression …	✓ Solved
An electron in hydrogen atom transitions from n = 3 to n …	✓ Solved
What are X-rays? Explain characteristic and continuous X-…	✓ Solved
What is the Franck-Hertz experiment? Explain how it valid…	✓ Solved
Explain spectral series in hydrogen atom. Write the formu…	✓ Solved
What is the difference between emission and absorption sp…	✓ Solved

Showing 6 of 6 questions

Q1: Explain Bohr's model of hydrogen atom. Derive expression for energy levels and radius of orbit.

Bohr's Model (1913): Atom with nucleus at center and electrons in circular orbits, combining classical mechanics with quantum postulates. Postulates: 1. Electron moves in circular orbit without radiating energy 2. Only orbits with angular momentum L = nℏ are allowed (n = 1, 2, 3, ...) where ℏ = h/(2π) = 1.055 × 10⁻³⁴ J·s 3. Radiation emitted when electron transitions between orbits Derivation of Orbital Radius: Coulomb force provides centripetal force: ke²/r² = m_e v²/r ke²/r = m_e v² ... (...

Q2: An electron in hydrogen atom transitions from n = 3 to n = 1. Find the energy and wavelength of photon emitted.

Given: Initial state: n_i = 3 Final state: n_f = 1 Energy levels: E_n = -13.6 eV/n² Energy of Initial Level: E₃ = -13.6/3² = -13.6/9 = -1.51 eV Energy of Final Level: E₁ = -13.6/1² = -13.6 eV Energy of Emitted Photon: ΔE = E_f - E_i = E₁ - E₃ ΔE = -13.6 - (-1.51) = -13.6 + 1.51 = -12.09 eV The energy released (emitted) = 12.09 eV Alternatively: ΔE = 13.6[1/n_f² - 1/n_i²] = 13.6[1/1 - 1/9] ΔE = 13.6[1 - 1/9] = 13.6 × 8/9 = 12.09 eV Frequency of Photon: hν = ΔE = 12.09 eV = 12.09 × 1.6 × 10⁻...

Q3: What are X-rays? Explain characteristic and continuous X-ray spectra.

X-rays: Electromagnetic radiation produced when high-energy electrons strike a metal target, with wavelengths 0.1-100 nm. Production: 1. Electrons accelerated through high potential difference (10 kV - 100 kV) 2. Directed at metal target (Cu, Mo, W, etc.) 3. Electrons decelerate and lose energy 4. Energy converted to X-ray photons Continuous X-ray Spectrum (Bremsstrahlung): - Produced by deceleration of electrons - Continuous distribution of wavelengths - Minimum wavelength λ_min when entire e...

Q4: What is the Franck-Hertz experiment? Explain how it validates Bohr's energy level concept.

Franck-Hertz Experiment (1914): Demonstrated quantized energy levels in atoms by measuring electron-atom collisions. Setup: - Mercury vapor in glass tube - Electrons emitted from cathode with adjustable voltage - Electrons accelerated toward anode through mercury vapor - Current measured vs accelerating voltage Procedure: 1. Electrons accelerated from cathode by voltage V 2. Electron kinetic energy: K.E. = eV 3. Electrons collide with Hg atoms 4. At low voltages: elastic collisions (little ene...

Q5: Explain spectral series in hydrogen atom. Write the formula and find the wavelengths of Hα and Hβ lines.

Spectral Series: Groups of spectral lines produced by transitions to the same lower level. General Formula (Rydberg): 1/λ = R_H[1/n_f² - 1/n_i²] Where: R_H = Rydberg constant = 1.097 × 10⁷ m⁻¹ = 0.01097 nm⁻¹ n_f = final level (lower) n_i = initial level (upper), n_i > n_f Spectral Series: 1. Lyman series: n_f = 1 (ultraviolet region) 1/λ = R_H[1 - 1/n²], n = 2, 3, 4, ... Lα: n = 2 → 1, λ = 121.6 nm 2. Balmer series: n_f = 2 (visible region) 1/λ = R_H[1/4 - 1/n²], n = 3, 4, 5, .....

Q6: What is the difference between emission and absorption spectra? Explain continuous, line, and band spectra.

Emission Spectrum: Spectrum of light emitted directly from a hot source. Absorption Spectrum: Spectrum of light after passing through absorbing material; shows dark lines on bright background. Types of Spectra: 1. Continuous Spectrum: - Unbroken distribution of all wavelengths - Produced by incandescent solid, liquid, or dense gas - Thermal radiation (blackbody radiation) - Temperature determines color and intensity - Examples: sunlight, tungsten bulb filament 2. Line Spectrum ...

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