MHT CET · Physics · Dual Nature of Matter
If the potential difference used to accelerate electrons is increased four times, by what factor does the de-Broglie wavelength associated with the electrons change?
- A Wavelength increased two times
- B Wavelength decreased to half
- C Wavelength increased four times
- D Wavelength remains the same
Answer & Solution
Correct Answer
(B) Wavelength decreased to half
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll}
& \lambda \propto \frac{1}{\sqrt{\mathrm{~V}}} \\
\therefore & \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{\mathrm{V}_1}{\mathrm{~V}_2}}
\end{array}\)
Given that, \(\mathrm{V}_2=4 \mathrm{~V}_1\)
\(\therefore \quad \lambda_2=\lambda_1 \times \sqrt{\frac{\mathrm{V}_1}{4 \mathrm{~V}_1}}=\frac{\lambda_1}{2}\)
& \lambda \propto \frac{1}{\sqrt{\mathrm{~V}}} \\
\therefore & \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{\mathrm{V}_1}{\mathrm{~V}_2}}
\end{array}\)
Given that, \(\mathrm{V}_2=4 \mathrm{~V}_1\)
\(\therefore \quad \lambda_2=\lambda_1 \times \sqrt{\frac{\mathrm{V}_1}{4 \mathrm{~V}_1}}=\frac{\lambda_1}{2}\)
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