ProSyllabusLearn a little. Grow every day.Log in
YOUR STUDY SPACE · CBSE

Atoms — Class 12 Physics

Physics Part II · Chapter 4

CBSE Class 12 community

View all
Physics, Chemistry, Maths + English
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Mathematics
  • Physics
  • + 3 more
~7 pages per kitPage 1 free
Physics, Chemistry, Biology + English
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Physics
  • Chemistry
  • + 3 more
~7 pages per kitPage 1 free
Physics
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Physics
~7 pages per kitPage 1 free
Accountancy, Business Studies, Economics + English
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Accountancy
  • Business Studies
  • + 3 more
~7 pages per kitPage 1 free
History
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • History
~7 pages per kitPage 1 free
Hindi Elective
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • हिंदी
~7 pages per kitPage 1 free
Mathematics
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Mathematics
~7 pages per kitPage 1 free
Sociology
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Sociology
~7 pages per kitPage 1 free
Economics
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Economics
~7 pages per kitPage 1 free
Home Science
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Home Science
~7 pages per kitPage 1 free
Urdu Elective
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • اردو
  • Urdu Elective
~7 pages per kitPage 1 free
Geography
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Geography
~7 pages per kitPage 1 free
Accountancy
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Accountancy
~7 pages per kitPage 1 free
English Core
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Flamingo
  • Vistas
~7 pages per kitPage 1 free
Political Science
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Political Science
~7 pages per kitPage 1 free
Chemistry
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Chemistry
~7 pages per kitPage 1 free
Business Studies
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Business Studies
~7 pages per kitPage 1 free
Hindi Core
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • हिंदी
~7 pages per kitPage 1 free
संस्कृतम् (केन्द्रिकम्)
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
संस्कृत (ऐच्छिक)
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
اردو (کور)
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
Computer Science
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
Fine Art · Painting
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
TrendingStart now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
हिंदुस्तानी संगीत (गायन / वादन)
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
Biology
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
Informatics Practices
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
Biotechnology
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
सृजनात्मक लेखन और अनुवाद
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
हिंदुस्तानी संगीत (तबला / पखावज)
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
English Elective · Kaleidoscope
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
Psychology
~50days leftPre-boards · school dates varyDec 2026 · school-specific · tentative
Start now for December pre-boards. Reuse it for boards.
  • Space weighted by unit marks
  • Charts from the book's own data
  • Traps corrected
Only 7 pagesPage 1 free
Browse all Class 12 kits →

Chapter 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 ; and radiation of frequency is emitted or absorbed only during transitions between orbits. These yield quantised orbit radii and energies 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 ideas & 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, eV for hydrogen.
Spectral series
Groups of lines (Lyman, Balmer, Paschen) from transitions to a fixed level.
Rydberg formula
for hydrogen lines.

Extra questions & answers

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: , with

Give the energy of the nth level of hydrogen.

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 .

Write the Bohr frequency condition.

; 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?

; the radius increases as the square of the quantum number.

Name a limitation of the Bohr model.

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