Experimental Study of Photoelectric Effect

The minimum value of frequency of incident radiation required for the emission of photoelectrons from a metal surface is called the Threshold Frequency.

The minimum value of energy required for the emission of photoelectrons from a metal surface is called the Work Function.

The retarding potential (–V₀) for which the photocurrent becomes zero is called the Stopping Potential.

The limit of photocurrent at which the increase in photocurrent stops even if the collector plate potential (V) is increased is called the Saturation Current.

\[V_0=\frac{hv}{e}-\frac{\phi_0}{e}=\frac{K.E_{max}}{e}\]

\[\phi_0=hv_0=h\frac{c}{\lambda_0}\]

Setup:

• Monochromatic radiation of suitable frequency from source S falls on photosensitive plate C (cathode).
• Electrons emitted from C are collected at plate A (anode/collector), kept at positive potential.
• Photoelectrons flow in the outer circuit → microammeter shows deflection (measures photoelectric current).
• Quartz window allows UV light to enter the evacuated glass tube.

Effect of Intensity:

• Photoelectric current varies directly with intensity of incident light (more photons → more electrons).
• Graph: Linear relationship between photoelectric current and light intensity.

Effect of Potential:

• On increasing positive collector potential → photocurrent increases and reaches saturation current.
• Higher intensity → higher saturation current (more electrons).
• Even at zero potential, some current flows (electrons have kinetic energy).
• Applying negative potential reduces the current.

Stopping Potential (V₀)

• The minimum negative potential given to the collector to stop all photoelectrons is Stopping Potential.
• At stopping potential: \[K_{\max}=eV_{0}=\frac{1}{2}mv^{2}\]
• Stopping potential is independent of intensity (but depends on frequency).
• Higher frequency → larger stopping potential.

Effect of Frequency on Stopping Potential:

• Graph shows: V₀ varies linearly with frequency ν (for a given photosensitive material).
• There exists a threshold frequency ν₀ below which V₀ = 0 (no emission).
• Threshold frequency is a characteristic of the metal.

Laws of Photoelectric Emission:

1. If frequency of radiation < threshold frequency → no emission (regardless of intensity).
2. Maximum KE of photoelectrons depends on frequency of radiation, not intensity.
3. Saturation photocurrent increases with intensity, but is independent of frequency.
4. There is no time lag between incidence of radiation and emission of electrons.