Question

The ejection of the photoelectron from the silver metal in the photoelectric effect experiment can be stopped by applying the voltage of 0.35 V when the radiation 256.7 nm is used. Calculate the work function for silver metal.

Answer 1

Hint: There is a relationship between energy of the incident radiation and work function and it is as follows.
Energy of the incident radiation = Work function of a metal + Kinetic energy of the photoelectron.
From the above formula we can calculate the work function of a metal and it is as follows.
Work function of a metal = Energy of the incident radiation – Kinetic energy of the photoelectron.

Complete step by step answer:
- First we have to calculate the energy of the incident radiation from the give data in the question.
- The formula to calculate the energy is as follows.
\[\begin{align}
 & E=hv \\
 & E=\dfrac{hc}{\lambda }\text{ }(\because v=\dfrac{c}{\lambda }) \\
\end{align}\]
Where E = Energy of the incident radiation
h = Planck’s constant
$\lambda $ = Wavelength of the radiation = 256.7 nm = 256.7$\times {{10}^{-9}}$ m
C = 3.0$\times {{10}^{-9}}$ m/s

- Substitute all the above known values in the above formula to get the energy of the incident radiation.
\[\begin{align}
 & E=\dfrac{hc}{\lambda } \\
 & =\dfrac{(6.626\times {{10}^{-34}})(3\times {{10}^{8}})}{256.7\times {{10}^{-9}}} \\
 & =7.74\times {{10}^{-19}}J \\
\end{align}\]

- We can convert the energy into electron volts (eV) by using the below relationship.
\[1eV=1.602\times {{10}^{-19}}J\]
- Therefore Energy of the incident radiation
\[\begin{align}
  & =\dfrac{(7.74\times {{10}^{-19}})}{(1.602\times {{10}^{-19}})} \\
 & =4.83eV \\
\end{align}\]

- By using energy of the incident radiation we can calculate the work function as follows.
Work function of a metal = Energy of the incident radiation – Kinetic energy of the photoelectron.
Work function of silver metal = 4.83 – 0.35 = 4.48 eV.
- Therefore the work function of silver metal is 4.48 eV.

Note: Without knowing the energy of the incident radiation we cannot calculate the work function of any metal. Energy of the incident radiation is the sum of the work function of a metal and kinetic energy of the photoelectron.