MHT CET · Physics · Dual Nature of Matter

If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie wavelength \((\lambda)\) associated with the electrons change?

A \(\lambda\) is increased to \(\sqrt{2}\) times.
B \(\lambda\) is increased to \(\frac{1}{\sqrt{2}}\) times.
C \(\lambda\) is decreased by \(\frac{1}{\sqrt{2}}\) times.
D \(\lambda\) is decreased by \(\sqrt{2}\) times.

Verified Solution

Answer & Solution

Correct Answer

(C) \(\lambda\) is decreased by \(\frac{1}{\sqrt{2}}\) times.

Step-by-step Solution

Detailed explanation

From \(\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mqV}}}\),
\(\lambda \propto \frac{1}{\sqrt{V}}\)
If potential difference is doubled, \(\lambda \propto \frac{1}{\sqrt{2 \mathrm{~V}}}\)
\(\therefore \quad \lambda\) is decreased by \(\frac{1}{\sqrt{2}}\) times.

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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