Class 12 Physics Chapter 12: Atoms

CBSE 2026–27 | NCERT-aligned free study resource

1. Rutherford’s Alpha-Particle Scattering Experiment

Rutherford’s experiment showed that most of the atom is empty space, while positive charge and most of the mass are concentrated in a tiny nucleus.

2. Limitations of Rutherford’s Model

Classical electrodynamics predicts that an accelerating electron should radiate energy and spiral into the nucleus. It also does not explain the discrete line spectrum of hydrogen.

3. Bohr’s Model

Bohr proposed that electrons occupy certain stationary orbits with quantised angular momentum. For hydrogen-like atoms, mvr = nh/2π. Electrons emit or absorb radiation when they transition between allowed energy levels.

4. Energy Levels

For hydrogen, E_n = −13.6/n² eV. The negative sign indicates a bound state. As n increases, the energy becomes less negative and approaches zero at ionisation.

5. Hydrogen Spectrum

Hydrogen emits light at specific wavelengths because its electron can occupy only discrete energy states. Different spectral series arise from transitions ending at particular lower levels.

6. Conceptual Connection

The chapter connects atomic structure with quantisation. Instead of a continuous range of allowed energies, an atom has discrete energy states. A spectral line is associated with a transition between two such states.

Worked Example

For a hydrogen electron transition from n=3 to n=2, use ΔE = 13.6(1/2² − 1/3²) eV to find the emitted photon energy, then use E = hc/λ if wavelength is required.

Common Exam Traps

• Bohr’s quantisation condition applies to allowed stationary states in the model.
• Energy becomes less negative as n increases.
• Emission occurs when an electron moves from a higher to a lower energy state.

Practice Questions

1. Describe Rutherford’s observations and conclusions.
2. Why did Rutherford’s model require modification?
3. State Bohr’s postulates.
4. Calculate the energy of an electron in a specified hydrogen orbit.
5. Explain the origin of hydrogen spectral lines.

Atomic Models & Visual Learning

Rutherford Scattering

Rutherford’s experiment established a small, dense, positively charged nucleus but could not explain atomic stability and line spectra.

Bohr Model

Bohr’s model quantises allowed orbits. Hydrogen spectral lines arise from transitions between permitted energy levels, with photon energy equal to the energy difference.

Worked Numerical

For a hydrogen transition from n=3 to n=2, use the Rydberg relation 1/λ=R(1/2²−1/3²) to calculate the emitted wavelength.

Common Mistakes

• Confusing orbit number n with energy directly without considering the negative energy convention.
• Using the wrong initial/final levels in the Rydberg equation.
• Assuming Rutherford’s model alone explains line spectra.

Practice

1. Calculate wavelength for a hydrogen transition.
2. Compare energy levels.
3. Explain Rutherford’s observations.
4. Explain why Bohr’s model improved the atomic model.