MHT CET · Physics · Dual Nature of Matter

In a photoelectric emission experiment, the stopping potential for a given metal is \(V\) volt, when radiation of wavelength \(\lambda\) is used. If radiation of wavelength \(2 \lambda\) is used with the same metal, then the stopping potential (in volt) will be
\(\text {[ } c \text { = velocity of light, } e=\text { charge on electron,}\) \( h=\text { Planck's constant }]\)

A \(V-\frac{h c}{2 e \lambda}\)
B \(V+\frac{h c}{2 e \lambda}\)
C \(\frac{V}{2}\)
D \(2 V\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(V-\frac{h c}{2 e \lambda}\)

Step-by-step Solution

Detailed explanation

According to Einstein's equation of photo-electric effect:
\(e V=\frac{h c}{\lambda}-\Phi---(1)\)
where, stopping potential is \(V, \lambda\) the incident wavelength and \(\Phi\) the work-function of the metal.

Now, if the incident wavelength is switched to \(2 \lambda\), the stopping potential can be written as
\(e V^{\prime}=\frac{h c}{2 \lambda}-\Phi---(2)\)
On subtracting equation (1) and (2), and subsequently rearranging:
\(V^{\prime}=V-\frac{h c}{2 \lambda e}\)

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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