Maharashtra State Board · Class 12 · Physics · Chapter 14

Dual Nature of Radiation and Matter — Formula Sheet

Board Formulas

10 formulas

1.Energy of a Photon★
$E = h ν = \frac{h c}{λ}$
$h$ : Planck's constant = 6.626×10⁻³⁴ J·s · $ν$ : Frequency of radiation (Hz) · $λ$ : Wavelength (m)
Photon carries a quantum of energy equal to Planck's constant times frequency.
2.Momentum of a Photon
$p = \frac{h}{λ} = \frac{h ν}{c}$
Photon has zero rest mass but non-zero momentum. Basis for de Broglie hypothesis.
3.Work Function
$φ_{0} = h ν_{0}$
Minimum energy needed to eject an electron from a metal surface.
4.Einstein's Photoelectric Equation★
$h ν = φ_{0} + K_{ma x} = φ_{0} + e V_{0}$
K_max = maximum KE of emitted electron. V₀ = stopping potential.
5.Stopping Potential★
$V_{0} = \frac{h}{e} ν - \frac{φ _{0}}{e}$
Linear graph of V₀ vs ν has slope h/e and x-intercept ν₀.
6.de Broglie Wavelength★
$λ = \frac{h}{p} = \frac{h}{m v}$
Matter wave: every particle of momentum p has an associated wavelength.
7.de Broglie Wavelength of Accelerated Electron
$λ = \frac{h}{2 m e V} \approx \frac{12.27}{V} A ˚$
V in volts, λ in ångströms. Handy shortcut for electron microscopy.
8.Threshold Frequency and Wavelength
$ν_{0} = \frac{φ _{0}}{h}, λ_{0} = \frac{h c}{φ _{0}}$
Below ν₀ (or above λ₀), no photoelectrons no matter how intense the light.
9.Number of Photons per Second
$n = \frac{P}{h ν} = \frac{P λ}{h c}$
P = radiant power (W). Useful when told the source power.
10.Compton Wavelength (reference)
$λ_{c} = \frac{h}{m _{e} c} = 2.43 \times 1 0^{- 12} m$
Characteristic length of the electron. Appears in Compton scattering.