Einstein's Photoelectric Equation Explained

Einstein proposed that light travels in small packets of energy called photons. When a photon hits a metal surface, it gives all its energy to a single electron. This energy is used in two ways:

1. Overcome the Work Function (φ): The minimum energy required to free an electron from the surface of the metal is called the Work Function (φ).
2. Kinetic Energy of the emitted electron: Whatever energy remains after overcoming the work function becomes the kinetic energy of the ejected electron.

The equation is:

KE_max = hν − φ

Where:

• KE_max = Maximum Kinetic Energy of the emitted photoelectron
• h = Planck's Constant (6.626 × 10⁻³⁴ J·s)
• ν (nu) = Frequency of the incident light
• φ (phi) = Work Function of the metal

Threshold Frequency (ν₀): The minimum frequency of light required to eject an electron from a metal surface. Below this frequency, no electrons are emitted regardless of how intense the light is.

• At threshold: KE = 0, so φ = hν₀
• The equation becomes: KE_max = h(ν − ν₀)

Why this was revolutionary: Before Einstein, the classical wave theory of light could NOT explain why:

• Electrons were not emitted below a certain frequency.
• Kinetic energy of electrons depended on frequency, not intensity.

Einstein's photon model perfectly explained all these observations.