MHT CET · Physics · Dual Nature of Matter

When certain metal surface is illuminated with a light of wavelength $λ$ , the stopping potential is V, when the same surface is illuminated by light of wavelength $2 λ$ , the stopping potential is $(\frac{V}{3})$ . The threshold wavelength for the surface is

A $\frac{8 λ}{3}$
B $\frac{4 λ}{3}$
C $4 λ$
D $6 λ$

Verified Solution

Answer & Solution

Correct Answer

(C) $4 λ$

Step-by-step Solution

Detailed explanation

Given for a metal, wavelength of light used =

λ

stopping potential =V
If

λ_{0}

be the threshold wavelength, then maximum kinetic energy of emitted electrons

K_{m a x} = h c (\frac{1}{λ} - \frac{1}{λ_{0}})

…(i)
Again, wavelength of used light

λ^{'} = 2 λ

Stopping potential, V’

= \frac{V}{3}

then

K_{m a x} = h c (\frac{1}{λ}, \frac{1}{λ_{0}})

\Rightarrow e V^{'} h c (\frac{1}{2 λ} - \frac{1}{λ_{0}})

\Rightarrow \frac{e V}{3} = h c (\frac{1}{2 λ}, \frac{1}{λ_{0}})

…. (ii)
From Eqs. (i) and (ii), we have

\frac{e V}{\frac{e V}{3}} = \frac{h c (\frac{1}{λ} - \frac{1}{λ_{0}})}{h c (\frac{1}{2 λ}, \frac{1}{λ_{0}})}

3 (\frac{1}{2 λ} - \frac{1}{λ_{0}}) = \frac{1}{λ} - \frac{1}{λ_{0}}

\Rightarrow λ_{0} = 4 λ

So, threshold wavelength is 4 times of wavelength of ligh.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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When certain metal surface is illuminated with a light of wavelength λ , the stopping potential is V, when the same surface is illuminated by light of wavelength 2λ , the stopping potential is V3 . The threshold wavelength for the surface is

Step-by-step Solution

When certain metal surface is illuminated with a light of wavelength $λ$ , the stopping potential is V, when the same surface is illuminated by light of wavelength $2 λ$ , the stopping potential is $(\frac{V}{3})$ . The threshold wavelength for the surface is