Question

A light of wavelength $5000A^\circ $ falls on a sensitive plate with work function $1.7eV$. Find the
(a) Energy of photon
(b) Energy of photoelectrons
(c) Stopping potential

Answer 1

Hint: In this question we are provided with a light with some wavelength and we have to find the energy of the photon, energy of the photoelectron and the stopping potential. Then we are using the formula which is given below in the formula used and with substituting the given values we can find our solution.

Formula used:
Energy of a photon $E = hf$
where h is the planck's constant and f is the frequency of the photon
$K.E = E - \phi $
where $E$ is the energy of photon and $\phi $ is the work function
$K.E = e{V_0}$
where ${V_0}$ is the stopping potential

Complete step by step solution:
(a) ENERGY OF PHOTON $\left( E \right)$: $E = h\upsilon $
$E = h\dfrac{c}{\lambda }$ $\left( {\because \upsilon = \dfrac{c}{\lambda }} \right)$ $K.E = E - \phi $
We had wavelength $\left( \lambda \right)$ be
$
\lambda = 5000A^\circ \\
\Rightarrow \lambda = 5000 \times {10^{ - 10}}m \\ $
planck's constant $h = 6.634 \times {10^{ - 34}}Js$ and speed of light be $c = 3 \times {10^8}m{s^{ - 2}}$
Putting the values
$E = \dfrac{{6.634 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{5000 \times {{10}^{ - 10}}}}J$
Now converting the energy into $eV$ by multiplying it with charge of the electron $1.6 \times {10^{ - 19}}$
$
E = 3.98 \times {10^{ - 13}}J \\
\Rightarrow E = \dfrac{{3.98 \times {{10}^{ - 13}}}}{{1.6 \times {{10}^{ - 19}}}}eV \\
\Rightarrow E = 2.48eV $

(b) ENERGY OF PHOTOELECTRON $\left( {K.E} \right)$
$K.E = E - \phi $
where $\phi $ is the work function which is already given in the question to be $1.7eV$
$
K.E = \left( {2.48 - 1.7} \right)eV \\
\Rightarrow K.E = 0.78eV $

(c) STOPPING POTENTIAL $\left( {{V_0}} \right)$
Using the formula $K.E = e{V_0}$
Now, substituting the above values
$
0.78eV = e{V_0} \\
\Rightarrow {V_0} = \dfrac{{0.78eV}}{e} \\
\therefore{V_0} = 0.78V
 $

Note: When we are working with small systems then $eV$ is so useful. Stopping potential is the potential need to stop the electron from removing when the incident photon has more energy than the work function of the metal. Work function is defined as the minimum work required to remove the electron from the solid.