Question

Silver has a work function of 4.7 eV. When ultraviolet light of wavelength 100 nm is incident upon it, a potential of 7.7 V is required to stop the photoelectrons from reaching the collector plate. How much potential will be required to stop the photoelectrons when light of wavelength 200 nm is incident upon silver?

• A. 1.5 V
• B. 3.85 V
• C. 2.35 V
• D. 15.4 V

Answer 1

The correct option is A 1.5 V

Einstein's equation for photoelectric effect is given by, $e{V}_0=E-W$

In first case: $e{V}_0=7.7eV,$ where $V_0$ is the cut-off potential and

$W=4.7eV$, work function of silver metal.

So, Energy of photon is $E_1=E=e{V}_0+W=7.7+4.7=12.4eV$

We know that $E=\frac{hc}{\lambda }$

If $E_2$ is the photon energy in the second case, $\frac{E_2}{E_1}=\frac{{\lambda }_1}{{\lambda }_2}=\frac{100nm}{200nm}=0.5$

so $E_2=0.5E_1=0.5\left(12.4\right)=6.2eV$

If $V_{02}$ is the cut-off potential in the second case, $e{V}_{01}=E_2-W$ (as same metal for both case so W is same for both case)

or $e{V}_{02}=6.2-4.7=1.5eV$

or $V_{02}=1.5V$