Question

When a centimeter thick surface is illuminated with light of wavelength $\lambda$ the stopping potential is $V.$ When the same surface is illuminated by light of wavelength $2\lambda$ the stopping potential is $\frac{V}{3}.$ The threshold wavelength for the surface is-

• A. $\frac{4\lambda }{3}$
• B. $4\lambda$
• C. $6\lambda$
• D. $\frac{8\lambda }{3}$

Answer 1

The correct option is B $4\lambda$

From, Einstein's photoelectric equation,

$\frac{hc}{\lambda }=\varphi +eV......\left(1\right)$

$\frac{hc}{2\lambda }=\varphi +\frac{eV}{3}.......\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we get,

$\Rightarrow (\frac{3}{2}-1)\frac{hc}{\lambda }=2\varphi$

$\Rightarrow \varphi =\frac{hc}{4\lambda }=\frac{hc}{{\lambda }_0}$

$\therefore {\lambda }_0=4\lambda$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(\text{B}\right)$ is the correct answer.