MHT CET · Physics · Dual Nature of Matter

When light of wavelength $\lambda$ is incident on photosensitive surface, the stopping potential is $V$. When light of wavelength $3 \lambda$ is incident on same surface, the stopping potential is $\frac{V}{6}$. Threshold wavelength for the surface is

A $2 λ$
B $3 λ$
C $4 λ$
D $5 λ$

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Answer & Solution

Correct Answer

(D) $5 λ$

Step-by-step Solution

Detailed explanation

Using

\frac{h c}{λ} - ϕ = e V

When, wavelength

λ

is incident on metallic surface, the sopping potential required to stop most energetic electron is

V

and when wavelength increases to

3 λ

, stopping potential required as

\frac{V}{6}

∴ \frac{h c}{λ} = e V + ϕ

..... (i)
And

\frac{h c}{3 λ} = \frac{e V}{6} + ϕ

.... (ii)
Thus equation (ii) can be rewritten as

\frac{2 h c}{λ} = e V + 6 ϕ

..... (iii)
Subtracting equation (i) from (iii) we get

\frac{h c}{λ} = 5 ϕ

and

ϕ = \frac{h c}{λ_{0}}

Thus

λ_{0} = 5 λ

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 light of wavelength \(\lambda\) is incident on photosensitive surface, the stopping potential is \(V\). When light of wavelength \(3 \lambda\) is incident on same surface, the stopping potential is \(\frac{V}{6}\). Threshold wavelength for the surface is

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