Question

A certain metallic surface is illuminated with monochromatic light of wavelength, $\lambda$. The stopping potential for photo-electric current for this light is $3V_0$. If the same surface is illuminated with light of wavelength $2\lambda$, the stopping potential is $V_0$. The threshold wavelength for this surface for photo-electric effect is:

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

Answer 1

The correct option is D $4\lambda$

From photoelectric equation,

$K.E{.}_{max}=h\nu -h{\nu }_{threshold}$...(i)

where $\nu$ is frequency of light $\nu =\frac{c}{\lambda }$

from equation (i)

$3e{V}_{\circ }=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_{threshold}}$...(ii)

$e{V}_{\circ }=\frac{hc}{2\lambda }-\frac{hc}{{\lambda }_{threshold}}$...(iii)

multiplying (iii) by 3 and subtracting (ii)

$0=\frac{hc}{2\lambda }-\frac{2hc}{{\lambda }_{threshold}}$

${\lambda }_{threshold}=4\lambda$