What traumatic event does Zitkala-Sa describe at the school?

The forcible cutting of her long hair

Why was the cutting of her hair so humiliating to Zitkala-Sa?

Among her people, shingled hair was worn by cowards and mourners

What did Rutherford's experiment establish?

That the atom has a tiny, dense, positively charged nucleus containing most of its mass.

Why is the classical atom unstable?

An orbiting electron should continuously radiate energy and spiral into the nucleus.

State Bohr's quantisation condition.

Angular momentum is quantised: \(mvr=n\dfrac{h}{2\pi}\), with \(n=1,2,3,\ldots\)

Give the energy of the nth level of hydrogen.

\(E_n=-\dfrac{13.6}{n^2}\) eV; negative, indicating a bound electron.

What is the ionisation energy of hydrogen?

13.6 eV, the energy needed to remove the electron from the ground state.

Which series of hydrogen lies in the visible region?

The Balmer series, from transitions to \(n=2\).

Write the Bohr frequency condition.

\(h\nu=E_i-E_f\); a photon is emitted or absorbed in a transition between levels.

Why are atomic spectra discrete?

Because electrons occupy only quantised energy levels, so transitions give specific frequencies.

How does orbit radius depend on n?

\(r_n\propto n^2\); the radius increases as the square of the quantum number.

CBSE Class 12 Board Examination

Q: Name a limitation of the Bohr model.

It fails for multi-electron atoms and cannot explain spectral fine structure or intensities.

Board examination for Class 12 students under CBSE, a crucial exam for higher education and career opportunities, covering stream-specific subjects.

Atoms — Class 12 Physics

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Chapter 4: Atoms

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Summary

Rutherford's alpha-scattering experiment showed that an atom's positive charge and nearly all its mass are concentrated in a tiny dense nucleus, with electrons orbiting in the surrounding space. However, classical physics predicted that orbiting electrons should radiate energy and spiral inward, making such an atom unstable—and it could not explain the sharp line spectra of gases. Bohr resolved this for hydrogen with three postulates: electrons occupy stationary orbits without radiating; angular momentum is quantised as \(mvr=n\dfrac{h}{2\pi}\); and radiation of frequency \(\nu=(E_i-E_f)/h\) is emitted or absorbed only during transitions between orbits. These yield quantised orbit radii and energies \(E_n=-\dfrac{13.6}{n^2}\) eV, explaining the hydrogen spectral series—Lyman, Balmer, Paschen and others—through the Rydberg formula. The energy-level diagram and the concepts of ground and excited states follow naturally. Though the Bohr model succeeds beautifully for hydrogen and hydrogen-like ions, it fails for multi-electron atoms and cannot explain spectral fine structure, foreshadowing the need for full quantum mechanics, yet it remains a milestone in understanding atomic structure.

Rutherford's nuclear modelFailure of classical modelBohr's postulatesEnergy levels of hydrogenHydrogen spectral seriesLimitations of the Bohr model

Key terms

Nucleus

Tiny dense central core holding the atom's positive charge and most of its mass.

Alpha-scattering

Rutherford's experiment revealing the nuclear model of the atom.

Bohr's postulates

Stationary orbits, quantised angular momentum, and quantum jumps with photon emission.

Energy level

Discrete allowed energy of an electron, \(E_n=-13.6/n^2\) eV for hydrogen.

Spectral series

Groups of lines (Lyman, Balmer, Paschen) from transitions to a fixed level.

Rydberg formula

\(\dfrac{1}{\lambda}=R\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)\) for hydrogen lines.

Important questions

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Practice quiz

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Class 12 Physics — Atoms (Practice Quiz)

10 Qs · ~10 min