Work Function Formula — Photoelectric Effect

Work Function (φ) is defined as the minimum amount of energy needed to liberate one electron from the surface of a metal.

Formula: φ = hν₀

Where:

• φ (phi) = Work function (measured in Joules or electron volts, eV)
• h = Planck's constant = 6.626 × 10⁻³⁴ J·s
• ν₀ (nu-zero) = Threshold frequency = minimum frequency of light that can cause photoelectric emission (in Hz)

Conversion: 1 eV = 1.6 × 10⁻¹⁹ J

Einstein explained the photoelectric effect (1905) using the concept of photons. When a photon of frequency ν hits a metal surface:

hν = φ + KE_max

hν = hν₀ + ½mv²_max

Where:

• hν = energy of incident photon
• φ = hν₀ = work function (energy used to free the electron from the metal)
• ½mv²_max = maximum kinetic energy of the emitted photoelectron

Rearranging: KE_max = h(ν − ν₀)

This shows that kinetic energy of emitted electrons depends only on frequency, not on intensity of light.

Caesium has the lowest work function — which is why it is used in photoelectric cells (LDRs and solar cells).

Stopping Potential (V₀) is the minimum reverse voltage applied to stop all photoelectrons:

eV₀ = KE_max = hν − φ

V₀ = (hν − φ) / e

This is experimentally measurable and confirms Einstein's equation.