Question

When a metallic surface is illuminated with light of wavelength $\lambda$, the stopping potential is $X$ volt. When the same surface is illuminated by light of wavelength $2\lambda$, the stopping potential is $\frac{x}{3}$. Threshold wavelength for the metallic 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 $4\lambda$

The Einstein equation for photo electric effect is $\frac{e{V}_0}{hc}=\frac{1}{\lambda }-\frac{1}{{\lambda }_0}$

Where $V_0$ is stopping potential and ${\lambda }_0$ is threshold wavelength. $h$ and $c$ are also constants.

For case-1

$\frac{eX}{hc}=\frac{1}{\lambda }-\frac{1}{{\lambda }_0}$ .....(1)

For case-2

$\frac{eX}{3hc}=\frac{1}{2\lambda }-\frac{1}{{\lambda }_0}$ .....(2)

dividing equation-1 by equation-2

we get $3=\frac{\frac{1}{\lambda }-p}{\frac{1}{2\lambda }-p}$ ,

Where $p=\frac{1}{{\lambda }_0}$, for simplicity.

Solving above equation we get $p=\frac{1}{4\lambda }$

or threshold wavelength ${\lambda }_0=4\lambda$