QJEEM20Ph7b6b: JEE Main 2020 Physics - Class 12 JEEM20Ph7b6b Solution: When radiation of wavelength is used to illuminate a metallic…

Question

Verified Solution • 2025–26 Session moderate

When radiation of wavelength

\lambda

is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3

\lambda

, the stopping potential is

{V \over 4}

. If the threshold wavelength for the metallic surface is n

\lambda

then value of n will be __________.

Accepted Answer

{{hc} \over \lambda } - \phi

= eV .....(i)

{{hc} \over {3\lambda }} - \phi = {{eV} \over 4}

.....(ii)

From (i) and (ii),

{{hc} \over {3\lambda }} - \phi =

{{hc} \over {4\lambda }} - {\phi \over 4}

\Rightarrow

{{hc} \over \lambda }\left( {{1 \over 3} - {1 \over 4}} \right) = {{3\phi } \over 4}

\Rightarrow

{{hc} \over {9\lambda }} = \phi

Also,

\phi

=

{{hc} \over {{\lambda _0}}}

\therefore

{{hc} \over {9\lambda }} = {{hc} \over {{\lambda _0}}}

\Rightarrow

\phi

= 9

\lambda

So, n = 9

Step-by-Step Verified Solution