MHT CET · Physics · Dual Nature of Matter

If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with the electrons change?

A Wavelength is decreased to \(\frac{1}{3}\) times.
B Wavelength is increased to \(\frac{1}{2}\) times.
C Wavelength is increased to \(\frac{1}{\sqrt{2}}\) times.
D Wavelength is decreased to \(\frac{1}{\sqrt{2}}\) times.

Verified Solution

Answer & Solution

Correct Answer

(D) Wavelength is decreased to \(\frac{1}{\sqrt{2}}\) times.

Step-by-step Solution

Detailed explanation

The de Broglie wavelength is given by
\(\lambda(\text { in } \mathrm{nm})=\frac{1.23}{\sqrt{V}}\)
Hence it becomes \(\frac{1}{\sqrt{2}}\) 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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