COMEDK · Physics · 27. Dual Nature of Matter

The velocity of an electron so that its momentum is equal to that of a photon of wavelength \(660 \mathrm{~nm}\) is

A \(1098 \mathrm{~ms} ^{-1}\)
B \(109 \mathrm{~ms} ^{-1}\)
C \(109.88 \mathrm{~cm} \mathrm{~s}^{-1}\)
D \(1098 \mathrm{~cm} \mathrm{~s}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(1098 \mathrm{~ms} ^{-1}\)

Step-by-step Solution

Detailed explanation

The momentum of a photon is given by \(p = \dfrac{h}{\lambda}\). Given \(\lambda = 660 \text{ nm} = 660 \times 10^{-9} \text{ m}\). The momentum of an electron is \(p = mv\). Equating the two: \(mv = \dfrac{h}{\lambda}\) \(v = \dfrac{h}{m \lambda}\) Substituting the values…

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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