JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Modern Physics

A metallic surface is illuminated with radiation of wavelength

λ

, the stopping potential is

V_{o}

. If the same surface is illuminated with radiation of wavelength

2 λ

, the stopping potential becomes

\frac{V _{o}}{4}

. The threshold wavelength for this metallic surface will be -

Answer: (D)

Solution

Einstein's equation gives

e V_{0} = \frac{h c}{λ} - \frac{h c}{λ _{0}}

for wavelength

λ

and

\frac{e V _{0}}{4} = \frac{h c}{2 λ} - \frac{h c}{λ _{0}}

for wavelength

2 λ

. Subtracting the second from the first,

\frac{3 e V _{0}}{4} = \frac{h c}{2 λ}

, so

e V_{0} = \frac{2 h c}{3 λ}

. Substituting back,

\frac{h c}{λ _{0}} = \frac{h c}{λ} - \frac{2 h c}{3 λ} = \frac{h c}{3 λ}

, hence the threshold wavelength is

λ_{0} = 3 λ

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option