Question

When a centimeter thick surface is illuminated with ligh of wavelength $\lambda$, the stopping potential is V. When the same surface is illuminated by light of wavelengh$2\lambda$, the stopping potential is V/3. The threshold wavelength for he 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 $4\lambda$

According to question,

$ev=h_0(\frac{1}{\lambda }-\frac{1}{{\lambda }_0})$

(i) $\frac{ev}{3}=h_c(\frac{1}{2\lambda }-\frac{1}{{\lambda }_0})$

(ii) Dividing equ $\left(1\right)$ by eq $\left(2\right)$

We get $3=\frac{(\frac{1}{\lambda }-\frac{1}{{\lambda }_0})}{(\frac{1}{2\lambda }-\frac{1}{{\lambda }_0})}$

or $\frac{3}{2\lambda }-\frac{1}{\lambda }=\frac{3}{{\lambda }_0}-\frac{1}{{\lambda }_0}$

$\Rightarrow \frac{1}{2\lambda }=\frac{2}{{\lambda }_0}$

Threshold wavelength for metallic surface

${\lambda }_0=4\lambda$