Question

Silver has a work function of $4.7\text{eV}$. When ultraviolet light of wavelength $100\text{nm}$ is incident upon it, a potential of $7.7\text{V}$ 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 $200\text{nm}$ is incident upon silver?

• A. $1.5\text{V}$
• B. $3.85\text{V}$
• C. $2.35\text{V}$
• D. $15.4\text{V}$

Answer 1

The correct option is A $1.5\text{V}$

We know that $E=\frac{hc}{\lambda }$ $\therefore E_1=12.375\text{eV}$
Similarly,
$E_2=\frac{1237.5}{{\lambda }_2}\text{eV.nm}=\frac{12375}{2000}=6.1875\text{eV}$


Put the values of $E_1$ and $E_2$ in Einstein's equation,
Now Case 1,
$E_1-W_0=e{V}_0$
$12.375-W_0=7.7\text{eV}$
$W_0=4.675\text{eV}$
and
Case 2,
$E_2-W_0=e{V}_s$
Hence,
$6.1875-W_0=e{V}_s^{\prime }$
Solving , we get $V_s^{\prime }\approx 1.5\text{V}$