Question

If we double the frequency of incident photon on photo-electric material then the ________.

1. Saturation photocurrent doubled
2. Saturation photocurrent becomes more than double
3. Cut-off voltage becomes more than double
4. Stopping potential doubles

Answer 1

Correct Answer - Option 4 : Stopping potential doubles

CONCEPT:

• Photoelectric effect: The photoelectric effect is a phenomenon where electrons are ejected from a metal surface when the light of sufficient frequency is incident on it. These ejected electrons are called photoelectrons.
  • When a photon falls on the metal surface, the photon’s energy is transferred to the electron.
  • Some part of the energy gets utilized in removing the electron from the metal surface, and the remaining goes into giving kinetic energy for the ejected electron.
• Work function (ϕ): It is the minimum amount of energy required to cause photo-emission of electrons from a metal surface when light is incident on it.
• Einstein’s Photoelectric Equation gives the relationship between work function (ϕ), the kinetic energy of the emitted electron, and the energy of the photon (E).

E = ϕ + KE

CALCULATION:

• The cutoff voltage in photoelectric emission is the minimum negative voltage that must be applied to the cathode in order to stop the photoelectric emission
• The relationship between the cutoff voltage and frequency is given by

⇒ eV₀ = h (ν - ν₀)

Where V₀ = Cutoff voltage, ν = frequency ν₀ = Threshold frequency

The above equation can be rewritten as

⇒ hν = eV₀ + hν ₀

If the frequency is doubled ν = 2ν in the above equation,  and assume new cutoff voltage as V₁, then the above equation becomes 

⇒ eV₁ = h(2ν - ν₀)

⇒ eV₁ = 2hν - hν₀

⇒ eV₁ = 2(eV₀ + hν₀) - hν₀

⇒ eV₁= 2eV₀ + 2hν₀ - hν₀

⇒ eV₁ = 2eV₀ + hν₀

• From the above equation, it is clear that the stopping potential is doubled 
• Hence, option 4 is the answer