Question

Calculate the work function of the surface.

Answer 1

Hint: Using Einstein's equation for photoelectric effect.
 $E=\dfrac{hc}{\lambda }-w$

Complete step by step solution:- Photoelectric effect:- the phenomenon of emission of electrons from metal under the effect of light rays is called photoelectric effect.
 First we using the Einstein’s equation for photoelectric effect:
 $e{{v}_{1}}=\dfrac{hc}{{{\lambda }_{1}}}-w$ ……………………(1)
Where $w=$ Work function
     $h=$ Plank’s constant
      $c=$ Speed of light
   ${{\lambda }_{1}}=$ Wavelength
    ${{v}_{1}}=$ Potential
    $e=$ Charge of electron
Work function does not depend on the wavelength of incident light.
 $w=\dfrac{hc}{{{\lambda }_{2}}}-e{{v}_{1}}$…………………(2)
Where $h=6.62\times {{10}^{-34}}joule\sec $
$c=3\times {{10}^{8}}\dfrac{m}{\sec }$
${{\lambda }_{2}}=5500\times {{10}^{-10}}m$
Putting these values in equation (2)
     $\begin{align}
  & w=\dfrac{6.62\times {{10}^{-34}}\times 3\times {{10}^{8}}}{5500\times {{10}^{-10}}}-\left( 1.6\times {{10}^{-19}}\times 0.19 \right) \\
 & w=\dfrac{6.62\times 3\times {{10}^{-34+8}}}{55\times {{10}^{-8}}}-\left( 0.204\times {{10}^{-19}} \right) \\
 & w=\dfrac{6.62\times 3\times {{10}^{-26+8}}}{55}-\left( 0.204\times {{10}^{-19}} \right) \\
 & w=0.36\times {{10}^{-18}}-0.204\times {{10}^{-19}} \\
 & w=3.6\times {{10}^{-19}}-0.204\times {{10}^{-19}} \\
 & w=3.3\times {{10}^{-19}}J \\
\end{align}$
To convert in electron volt (ev) divided by
  $\begin{align}
  & w=\dfrac{3.3\times {{10}^{-19}}}{1.6\times {{10}^{-19}}} \\
 & w=2.07ev \\
\end{align}$

Note:- Work function takes different cases for different cases for the same substance. When the electrons revolve around the nucleus they have some energy stored in them. There are forces acting on them pulling them towards the nucleus. You have to provide some energy to cancel out this energy that is holding the electron in the orbit. This minimum required energy is called the work function of that metal. The forces of attraction acting on the electrons vary according to the environmental conditions like temperature, pressure, etc. So, for different environmental conditions the work function of the same material can vary.