MHT CET · Physics · Dual Nature of Matter

Threshold frequency for a metal is \(15 \times 10^{14} \mathrm{~Hz}\). The light of wavelength \(6000 Å\) falls on the metal surface. Which one of the following statements is correct? [velocity of light, \(\left.\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right]\)

A photoelectrons are emitted with velocity c.
B photoelectrons come out with velocity \(3 \times 10^{6} \mathrm{~m} / \mathrm{s}\)
C photoelectrons come out with zero velocity.
D photoelectrons will not be emitted.

Verified Solution

Answer & Solution

Correct Answer

(D) photoelectrons will not be emitted.

Step-by-step Solution

Detailed explanation

\(v_{0} =15 \times 10^{14} \mathrm{~Hz} \)
\( \therefore \lambda_{0}=\frac{C}{v} =\frac{3 \times 10^{8}}{15 \times 10^{14}} \)
\( =2 \times 10^{-7} \mathrm{~m} \)
\( =2000\)Å
\( \lambda =6000\)Å
Since \(\lambda>\lambda_{0}\), photo electrons will not be emitted

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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