Question

Threshold wavelength depends upon:
a. Frequency of incident radiation
b. Velocity of electrons
c. Work function
d. None of these

Answer 1

Hint: Threshold wavelength is the maximum wavelength that the incident radiation must have in order to execute the photoelectric effect.

Complete Step by Step Solution:
Let us talk about the photoelectric effect first where the concept of threshold wavelength comes into picture.
Photoelectric effect is the emission of electrons when electromagnetic radiation such as light hits onto a material.
 Photoelectrons as a result are the electrons emitted as a result of the above process.
The photons of light which have this photon energy hit the surface; they actually have some photon energy which is proportional to the frequency of light.
So, in order to execute a photoelectric effect, the wavelength of the incident radiation should be lesser than the threshold wavelength of the surface, in most cases which is metal.
Let us look at the formula pertaining to the threshold wavelength:

\[\begin{align}
  & \Phi =h\times {{v}_{0}} \\
 & or \\
 & \Phi =\dfrac{{h}{c}}{{{\lambda }_{0}}}............Eqn1 \\
\end{align}\]

Where

${{v}_{0}}=\dfrac{c}{{{\lambda }_{0}}}$
Here in the above equations,

$\Phi =$ work function of surface

h= Planck’s constant = $6.63 \times 10^{-34}$ Js

${{v}_{0}}$ = Speed of light and ${{\lambda }_{0}}$ =threshold wavelength

Hence, from the above equation 1 we get,

Work function of the surface (metal or otherwise)

Therefore, it could be concluded that the threshold wavelength depends upon the work function.

Note: Threshold wavelength should not be confused with the threshold frequency which is, the minimum frequency of the incident radiation below which the photoelectric effect is not possible irrespective of the intensity of the incident radiation. Work function is basically the amount of work that is needed to be done to excite/remove an electron from a solid (surface metal or otherwise).