Chapter 27, Problem 27P

To determine

Work function of the metal.

Answer to Problem 27P

Solution:

Work function of the metal is $3.32\text{eV}$.

Explanation of Solution

Given:

Wavelength of the light, $\lambda =250\text{nm}$

Stopping voltage, $V=1.64\text{V}$

Formula used:

The maximum energy of the photon is calculated as

$W=\frac{hc}{e\lambda }$

Here,

$e$ is the charge of electron

$h=6.62\times {10}^{-34}\text{J-s}$ is the Planck’s constant

$c=3\times {10}^8\text{m/s}$ is the speed of light

$\lambda$ is the wavelength

The kinetic energy of the electron is calculated as

$KE=eV$

Here,

$V$ is the voltage

Calculation:

The maximum energy of the photon is calculated as

$W=\frac{hc}{e\lambda }$

Plugging the values in the above equation

$\begin{array}{c}W=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{1.6\times {10}^{-19}\times 250\times {10}^{-9}}\\ =4.96\text{eV}\end{array}$

The kinetic energy of the electron is calculated as

$KE=eV$

Plugging the values in the above equation

$\begin{array}{c}KE=e\times 1.64\\ =1.64\text{eV}\end{array}$

The work function of the metal is calculated as

$KE=W-W_o$

Plugging the values in the above equation

$\begin{array}{c}1.64=4.96-W_o\\ W_o=3.32\text{eV}\end{array}$