Question

At the threshold frequency, the velocity of the electron is:
A. Zero
B. Maximum
C. Minimum
D. Infinite

Answer 1

Hint: The threshold frequency is the minimum frequency of the light required by a metal to kick out electrons from it. If the frequency of light is less than threshold frequency, no electron will be kicked out of the metal.

Formula used:
$\begin{align}
  & K.E=h\nu -\phi \\
 & \phi =h{{\nu }_{\begin{smallmatrix}
 th \\
\end{smallmatrix}}} \\
\end{align}$

Complete step by step answer:
Let us assume the frequency of incident light as $\nu $ and threshold frequency as ${{\nu }_{th}}$. As per the above formula, $\phi $is the work function of the metal and it is equal to $h{{\nu }_{th}}$. Question says, if the threshold frequency is equal to frequency of incident light, what is the velocity of the electron. Clearly, $\nu ={{\nu }_{th}}$.
So, the kinetic energy of the electron becomes
$K.E=h\nu -h{{\nu }_{th}}$
As threshold frequency=frequency of light,
$\begin{align}
  & K.E=h\nu -h{{\nu }_{th}} \\
 & K.E=h\nu -h\nu \\
 & K.E=0 \\
 & \\
\end{align}$
We know the velocity of an electron is determined by its kinetic energy.
If the kinetic energy of the electron is zero, the velocity of the electron is also zero.
Hence, the correct answer is option A.

Additional Information
The kinetic energy of an electron is defined by the equation $E=\dfrac{1}{2}m{{v}^{2}}$ where $v$ is the velocity of the electron. When kinetic energy is zero, the velocity will also be equal to zero. Light with frequency equal to threshold frequency will eject the electron without any release of kinetic energy. If the frequency of light is more than the threshold frequency, kinetic energy is released with ejecting the electron. If the light frequency is lower than threshold frequency, no electron is ejected and no kinetic energy is produced.

Note:
The velocity of the electron depends on kinetic energy but not on the potential energy, so don’t get confused with both the energies. In the photoelectric effect, kinetic energy is used for finding the velocity of the electron.