Question

Explain the existence of threshold frequency of incident radiation for photoelectric emission from a given surface.

Hint:

The threshold frequency is the minimum frequency required to release photoelectrons from a material. Below this frequency, photons do not have enough energy to overcome the work function.

Answer 1

Step 1: The threshold frequency (\( \nu_{\text{th}} \)) is the minimum frequency of incident radiation required to emit photoelectrons from a given surface. This frequency corresponds to the minimum energy required to overcome the work function (\( \phi \)) of the material.
Step 2: According to Einstein’s photoelectric equation:
\[ E_{\text{photon}} = h \nu \] where \( E_{\text{photon}} \) is the energy of the incoming photon. For photoelectric emission to occur, the energy of the photon must be greater than or equal to the work function of the material, \( \phi \):
\[ h \nu \geq \phi \] Step 3: The threshold frequency \( \nu_{\text{th}} \) corresponds to the minimum frequency at which this condition is satisfied, i.e. when \( h \nu_{\text{th}} = \phi \). Thus, the threshold frequency is given by:
\[ \nu_{\text{th}} = \frac{\phi}{h} \] Step 4: If the frequency of the incident radiation is lower than the threshold frequency, the energy of the photons is insufficient to overcome the work function, and no photoelectrons are emitted.