Question

In photoelectric effect stopping potential is $3V_0$ for incident wavelength ${\lambda }_0$ and stopping potential for incident wavelength$2{\lambda }_0$. Find threshold wavelength.

• A. $3{\lambda }_0$
• B. $2{\lambda }_0$
• C. $4{\lambda }_0$
• D. $8\lambda$

Answer 1

The correct option is C

$4{\lambda }_0$

Solution:

Step 1: Given information

Stopping potential $=3V_0$

Incident wavelength $={\lambda }_0$

Incident wavelength$=2{\lambda }_0$

Step 2: Calculate the threshold wavelength

Knows, $KE=hv–W$

$\Rightarrow eV=\frac{hc}{\lambda –W}$

For the first case,

$\Rightarrow e\left(3V_o\right)=\frac{hc}{{\lambda }_o}–W$ ……….(i)

For the second case,

$\Rightarrow e\left(V_o\right)=\frac{hc}{2{\lambda }_o}–W)$…..…..(ii)

From equations (i) and (ii), we get,

$\Rightarrow W=\frac{hc}{\left(4{\lambda }_o\right)}$

$For{\lambda }_{th}$,

$\Rightarrow w=\frac{hc}{{\lambda }_{th}}$

$\Rightarrow \frac{hc}{\left(4{\lambda }_o\right)}=\frac{hc}{{\lambda }_{th}}$

$\Rightarrow {\lambda }_{th}=4{\lambda }_o$

Hence, the correct option is (C).