MHT CET · Physics · Dual Nature of Matter

Light of two different frequencies whose photons have energies \(1.3 \mathrm{eV}\) and \(2.8 \mathrm{eV}\) respectively, successfully illuminate a metallic surface whose work function is \(0.8 \mathrm{eV}\). The ratio of maximum speeds of emitted electrons will be

A \(1: 4\)
B \(1: 2\)
C \(1: 3\)
D 1:5

Verified Solution

Answer & Solution

Correct Answer

(B) \(1: 2\)

Step-by-step Solution

Detailed explanation

For maximum speed of the photo electrons, \(\frac{1}{2} m v^2=E_{\mathrm{P}}-\phi\) where \(\phi=0.8 \mathrm{eV}\) is the work function of the metal. Energy of photon \(E_1=1.3 \mathrm{eV}\)
\(
\therefore \frac{1}{2} m v_1^2=1.3-0.8 \mathrm{eV}
\)

Ratio of maximum speeds of the electrons can obtained by taking ratio of equation (1) and (2),
\(\therefore \frac{v_1^2}{v_2^2}=\frac{0.5}{2}=\frac{1}{4}\)
Or, \(\frac{v_1}{v_2}=\frac{1}{2}\)

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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