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
- Photoelectrons are emitted only when the frequency of the incident light is above critical frequency
- Number of photoelectrons emitted is larger for larger intensity. (Produced larger photocurrent)
- Stopping potential is independent of intensity
- 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.