Semiconductors & Modern Physics Notes

Last reviewed 16 Sept 2026 · 8 min read

Birth of quantum physics

Black body radiation

Classical physics failed to explain the spectrum of black body radiation (ultraviolet catastrophe).
Planck (1900): energy is emitted/absorbed in discrete packets (quanta):

E = h f = \frac{h c}{λ}, h = 6.626 \times 1 0^{- 34} J\cdots

$1 eV = 1.602 \times 1 0^{- 19}$ J; handy relation: $E (eV) \approx \frac{1240}{λ ( nm )}$ .

Photoelectric effect

Emission of electrons from a metal surface when light of sufficiently high frequency falls on it.

FormulaEinstein's photoelectric equation

h f = ϕ + K E_{ma x}, ϕ = h f_{0}

$ϕ$ = work function; $f_{0}$ = threshold frequency — no emission below $f_{0}$ , however intense the light
$K E_{ma x} = e V_{0}$ ( $V_{0}$ = stopping potential) — depends on frequency, not intensity
Photocurrent ∝ intensity (number of photons)
Emission is practically instantaneous

Confirms the particle (photon) nature of light (Einstein, Nobel Prize 1921).
Applications: photocells, light meters, solar cells, automatic street lights, burglar alarms, image sensors.

Compton effect

Scattering of X-rays by electrons increases wavelength: $Δ λ = \frac{h}{m _{e} c} (1 - cos θ)$ — further evidence of photon momentum $p = h / λ$ .

Matter waves

Formulade Broglie wavelength

λ = \frac{h}{p} = \frac{h}{m v}

For an electron accelerated through V volts: $λ = \frac{h}{2 m e V} \approx \frac{1.227}{V}$ nm

Confirmed by Davisson–Germer electron diffraction; basis of the electron microscope (SEM/TEM — very high resolution, used to study cement hydration products, microstructure).

Heisenberg's uncertainty principle

Δ x Δ p \geq \frac{h}{4 π}

Position and momentum cannot both be known exactly.

Atomic structure

Model	Key features / limitations
Thomson ("plum pudding")	Electrons embedded in positive sphere — disproved by scattering
Rutherford (1911)	Alpha scattering by gold foil → tiny dense positive nucleus; could not explain atomic stability or line spectra
Bohr (1913)	Electrons in stationary orbits with quantised angular momentum $m v r = nh /2 π$ ; radiation emitted when electrons jump between levels
Quantum mechanical model	Orbitals, quantum numbers (see Atomic Structure & Chemical Bonding)

FormulaHydrogen atom (Bohr model)

E_{n} = - \frac{13.6}{n ^{2}} eV, r_{n} = 0.529 n^{2} \overset{˚}{A}

Photon emitted: $h f = E_{n_{2}} - E_{n_{1}}$ Spectral series: Lyman (to n = 1, ultraviolet), Balmer (to n = 2, visible), Paschen, Brackett, Pfund (infrared)

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Birth of quantum physics

Black body radiation

Photoelectric effect

Compton effect

Matter waves

Heisenberg's uncertainty principle

Atomic structure

This chapter is in the syllabus of