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 electrons change?
- A Wavelength in increased to \(\frac{1}{\sqrt{2}}\) times.
- B Wavelength in increased to \(\frac{1}{2}\) times.
- C Wavelength in decreased to \(\frac{1}{\sqrt{2}}\) times.
- D Wavelength in decreased to \(\frac{1}{2}\) times.
Answer & Solution
Correct Answer
(C) Wavelength in decreased to \(\frac{1}{\sqrt{2}}\) 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.
\(\lambda \propto \frac{1}{\sqrt{V}}\)
If potential difference is doubled, \(\lambda \propto \frac{1}{\sqrt{2 \mathrm{~V}}}\)
\(\therefore \quad \lambda\) is decreased by \(\frac{1}{\sqrt{2}}\) times.
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