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What is the stopping potential when the metal with work function \[0.6eV\] is illuminated with the light of \[2\,eV\].
A. 2.6 V
B. 3.6 V
C. 0.8 V
D. 1.4 V

Last updated date: 23rd Apr 2024
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Hint: Stopping potential is the potential required to bring the electron to rest. Also, we can say that stopping potential is defined as the minimum negative voltage applied to the anode to stop the photocurrent. The maximum kinetic energy of the electrons equals the stopping voltage when measured in electron volt. Here we find the stopping potential by using the values of the energy of the incident photon and the work function. By using Einstein’s equation, we can solve this problem.

Formula used:
Kinetic energy of photoelectrons is given as:
\[KE = E - \phi \]
Where E is the energy and \[\phi \] is the work function.
Also, \[KE = e{V_0}\]
Where, \[{V_0}\] is the stopping potential.
1eV=\[1.6 \times {10^{ - 19}}J\]

Complete step by step solution:
Given Energy of the incident photon, \[E = 2eV\]
Work function, \[\phi = 0.6eV\]
By Einstein’s equation,
\[KE = E - \phi \]
Also, we can write,
\[E = \phi + KE\]
By using \[KE = e{V_0}\], we have
\[\begin{array}{l}E = \phi + e{V_0}\\ \Rightarrow {\rm{e}}{{\rm{V}}_0}{\rm{ = E - }}\phi \\ \Rightarrow {V_0} = \dfrac{{E - \phi }}{e}\end{array}\]
Substituting the values, we get
\[\begin{array}{l}{V_0} = \dfrac{{2eV - 0.6eV}}{e}\\ \therefore {V_0}{\rm{ = 1}}{\rm{.4V}}\end{array}\]
Therefore, the stopping potential will be 1.4V.

Hence option D is the correct answer

Additional Information: Stopping potential is the potential required to stop the photoelectric effect. Stopping potential is defined as the potential required for stopping the ejecting of an electron from a metal surface when the incident light energy is greater than the work potential of the metal. The intensity of incident radiation stopping potential does not depend. On increasing intensity, the value of saturated current increases, whereas the stopping potential remains unchanged. The stopping voltage can be used to determine the kinetic energy that the electrons have as they are ejected from the metal surface.

Note: In order to emit an electron from the surface of the metal, the energy of the electron must be greater than the work function. The work function is dependent on the nature of the metal and the conditions of the metal surface. It can be measured by the unit of energy known as electron volt (eV).