🌱 Digital Garden

Photoelectric Effect

Consequence of Plank’s quantum Hertz: discovered radio waves, observed emission of charged particles from metal on uv radiation

Lenard observed four facts when studying the photoelectric effect

  1. Photoelectrons are emitted only when the frequency of the incident light is above critical frequency
  2. Number of photoelectrons emitted is larger for larger intensity. (Produced larger photocurrent)
  3. Stopping potential is independent of intensity
  4. There is no time delay in emission of photoelectrons when the light source is turned on.

This is where wave theory had failed because it predicted that intensity of light↑ ⇒ energy↑ ⇒ emission of electrons; which is not true It also predicted that even with a dim light it is possible to eject an electron if we apply it long enough (buildup of energy); which doesn’t happen.

Photon #

If a photon has frequency ν then the energy it carries is E=hν

  • Speed: c=3â‹…10^-8 m/s
  • Rest mass: 0
  • Kinetic mass: $m=\frac{E}{c^2}$
  • Momentum: $p=\frac{E}{c}$

Work function #

Characteristic of the metal. The minimum frequency of light required to eject an electron from a metal surface: ν₀ threshold frequency W=Φ=hν₀ Cut-off wavelength: $\lambda_c=\frac{c}{\nu_0}$

Work function is usually less than or even half of ionization energy.

Kinetic Energy #

K.E.=Energy of photon-work function $K.E.=\frac{1}{2}m_ev^2=E-\Phi=h(\nu-\nu_0)$

A question #

Q. Suppose the frequency of light is less than the critical frequency, why can’t an electron absorb 2 photons and escape the metal?

Probability of an electron to absorb photons is very low (order of 1/1000), therefore the probability of an electron to absorb 2 photons is extremely small and is ignored.