Class 12 · Chapter 11
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
11 formulas across 3 topics in Dual Nature of Radiation & Matter.
Updated 2026-07-09 · v1.0.0
Einstein treated light as a stream of discrete energy packets — photons — each carrying a fixed energy and momentum set entirely by its frequency.
E = hν = hc/λ
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| h | Planck's constanth = 6.63 × 10⁻³⁴ J·s | J·s | [ML²T⁻¹] |
| ν | frequency of the radiation | Hz | [T⁻¹] |
Valid when
p = h/λ = E/c
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| p | momentum of the photon | kg·m/s | [MLT⁻¹] |
Valid when
W₀ = hν₀
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| W₀ | work function — minimum energy to free an electron from the metal surface | J or eV | [ML²T⁻²] |
| ν₀ | threshold frequency of the metal | Hz | [T⁻¹] |
Valid when
Einstein's photoelectric equation explains every observed feature of the photoelectric effect at once — features that classical wave theory could never account for.
hν = W₀ + KE(max) , KE(max) = h(ν − ν₀)
Energy conservation for a single photon absorbed by a single electron: photon energy = work to escape + leftover kinetic energy
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| KE(max) | maximum kinetic energy of emitted photoelectrons | J or eV | [ML²T⁻²] |
Valid when
Common mistakes
eV₀ = KE(max) = h(ν − ν₀)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| V₀ | stopping potential — the retarding voltage that just stops the fastest photoelectrons | V | [ML²T⁻³A⁻¹] |
| e | electronic charge | C | [AT] |
Valid when
Photon flux = P/(hν) , Photocurrent ∝ intensity (at fixed frequency)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n | number of photons incident per second | s⁻¹ | [T⁻¹] |
| P | power of the incident light beam | W | [ML²T⁻³] |
Valid when
If light (a wave) can behave like particles, de Broglie proposed the reverse: every moving particle should have an associated wavelength — matter and radiation are symmetric in this respect.
λ = h/p = h/(mv)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| λ | de Broglie wavelength | m | [L] |
| m | mass of the particle | kg | [M] |
Valid when
Common mistakes
λ = h / √(2mqV)
Kinetic energy gained qV = p²/2m, solved for p and substituted into λ = h/p
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| q | charge of the particle | C | [AT] |
| V | accelerating potential difference | V | [ML²T⁻³A⁻¹] |
Valid when
λ = h / √(2mkT) (thermal/uncharged particles, e.g. neutrons)
Average kinetic energy from kinetic theory, (3/2)kT, used in place of qV for a neutral particle in thermal equilibrium
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| k | Boltzmann constant | J/K | [ML²T⁻²Θ⁻¹] |
| T | absolute temperature | K | [Θ] |
Valid when
2πr = nλ
An electron orbit is stable only if it forms a whole number of de Broglie wavelengths around the circumference — otherwise the wave destructively interferes with itself
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| r | radius of the electron's orbit | m | [L] |
| n | principal quantum number | dimensionless (integer) | [M⁰L⁰T⁰] |
Valid when
Δλ = (h/m(e)c)(1 − cosθ)
Conservation of energy and momentum in a photon-electron collision, treating the photon as a particle with p=h/λ
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| Δλ | increase in wavelength of the scattered photon | m | [L] |
| m(e) | electron rest mass | kg | [M] |
| θ | scattering angle of the photon | rad | [M⁰L⁰T⁰] |
Valid when
The Davisson–Germer experiment (electron diffraction from a nickel crystal) is the direct experimental confirmation of de Broglie's hypothesis — boards frequently ask for its significance alongside the wavelength formulas.
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