MHT CET · Chemistry · Structure of Atom

What is de Broglie's wavelength for a particle having mass \(6.64 \times 10^{-27} \mathrm{~kg}\) moving with velocity of \(3 \times 10^3 \mathrm{~ms}^{-1} ?\left[\mathrm{~h}=6.63 \times 10^{-34} \mathrm{Js}\right]\)

A 0.111 nm
B 0.0333 nm
C 1.22 nm
D 2.42 nm

Verified Solution

Answer & Solution

Correct Answer

(B) 0.0333 nm

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \lambda=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}}{6.64 \times 10^{-27} \mathrm{~kg} \times 3 \times 10^3 \mathrm{~ms}^{-1}} \\ & =0.0333 \times 10^{-9} \mathrm{~m} \\ & =0.033 \mathrm{~nm}\end{aligned}\)

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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