Question

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

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

Answer 1

The correct option is D $1.5V$

From Einstein's Photoelectric equation,

$e{v}_0+\varphi =\frac{hc}{\lambda }$

and $e{v}_0+{\varphi }_0=\frac{hc}{{\lambda }^{\prime }}$

$\frac{e{v}_0^{\prime }+\varphi }{e{v}_0+\varphi }=\frac{\lambda }{{\lambda }^{\prime }}=\frac{100}{200}=\frac{1}{2}$

$2e{v}_0^{\prime }+2\varphi =e{v}_0+\varphi$

$e{v}_0^{\prime }=\frac{e{v}_0-\varphi }{2}=\frac{7.7-4.7}{2}=1.5V$