Dual Nature of Radiation and Matter — Formula Sheet

E = hν

φ₀ = hν₀

hν = φ₀ + K_max

K_max = h(ν − ν₀)

eV₀ = (1/2)mv²_max = K_max

λ = h/p = h/(mv)

λ = h/√(2mK)

λ = h/√(2qmV) = 12.3/√V Å

EXAMPLE 1 (NCERT type)

Sodium has work function φ₀ = 2.3 eV. Light of wavelength λ = 5×10⁻⁷ m is incident on it.

STEP 1 — Find Threshold Frequency

ν₀ = φ₀/h = (2.3 × 1.6×10⁻¹⁹) / (6.6×10⁻³⁴) = 3.68×10⁻¹⁹ / 6.6×10⁻³⁴ = 5.6×10¹⁴ Hz

STEP 2 — Find Energy of Photon

E = hc/λ = (6.6×10⁻³⁴ × 3×10⁸) / (5×10⁻⁷) = 1.98×10⁻²⁵ / 5×10⁻⁷ = 3.96×10⁻¹⁹ J

Light consists of photons — discrete packets of energy. Energy of each photon = hν.

Work function (φ₀) = minimum energy needed to release an electron from metal surface = hν₀.

Einstein's photoelectric equation

hν = φ₀ + K_max = hν₀ + eV₀.