Physics by Lamhi: Not Your Boring Physics

CLASS 12 · CHAPTER 12 · MODERN PHYSICS

QUICK REVISION

Atoms

Every key result from this chapter, boxed and ready for a last look before the exam. No derivations here, just what to recall and when to use it — for the full explanation, see the detailed notes.

1. Bohr's Postulates

  1. Electrons occupy stationary orbits with quantised angular momentum, L=mvr=nh/2πL=mvr=nh/2\pi, and do not radiate while in them.
  2. A photon is emitted or absorbed only on a jump between orbits: hν=Ei−Efh\nu = E_i - E_f.

2. Orbit Radius & Energy

Radius
rn=n2×0.529 A˚r_n = n^2 \times 0.529\ \text{\AA}
Energy
En=−13.6n2 eVE_n = -\dfrac{13.6}{n^2}\ \text{eV}

n=1 (ground state): E₁ = −13.6 eV, r₁ = 0.529 Å (the Bohr radius). Ionisation energy from the ground state = 13.6 eV.

3. The Shrinking-Gap Ladder — the exam trap

Intuition says higher levels should spread further apart. They don’t, the gaps shrink as n increases, converging toward E = 0 (ionisation) at n → ∞:

  1. n=1 → n=2: gap = 10.2000 eV (by far the largest gap)
  2. n=2 → n=3: gap = 1.8889 eV
  3. n=3 → n=4: gap = 0.6611 eV
  4. n=4 → n=5: gap = 0.3060 eV
  5. n=5 → n=6: gap = 0.1662 eV

See it live: interactive energy-level simulation →

4. Spectral Series

  1. Lyman (final level n=1): ultraviolet.
  2. Balmer (final level n=2): visible — the only series with visible lines.
  3. Paschen (final level n=3): infrared.

Within any series, lines bunch up toward a sharp series limit (transition from n=∞ to that series’ final level) as the starting level rises.

5. Quick Formula: Wavelength Shortcut

Photon energy ↔ wavelength
E(eV)=1240λ(nm)E(\text{eV}) = \dfrac{1240}{\lambda(\text{nm})}

Balmer series limit: E = 3.4000 eV → λ ≈ 364.7 nm. Lyman series limit (n=1): E = 13.6000 eV → λ ≈ 91.2 nm.

6. Limitations

Only accurate for hydrogen and other single-electron (hydrogen-like) ions — e.g. He⁺, Li²⁺. Fails once a second electron adds electron-electron repulsion to the picture.

Full derivations and worked examples: detailed notes →