MHT CET · Physics · Dual Nature of Matter
Electrons are accelerated through a potential difference of 16 kV . If the potential difference is increased to 64 kV , then de-Broglie wavelength associated with electron will
- A remain same.
- B becomes half.
- C becomes four time.
- D becomes quarter.
Answer & Solution
Correct Answer
(B) becomes half.
Step-by-step Solution
Detailed explanation
For an electron accelerated through potential V,
\(\begin{array}{ll}
& \lambda \propto \frac{1}{\sqrt{V}} \text { i.e. } \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{V_2}{v_1}} \\
\therefore & \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{64}{16}}=2 \\
\therefore & \lambda_2=\frac{\lambda_1}{2}
\end{array}\)
\(\begin{array}{ll}
& \lambda \propto \frac{1}{\sqrt{V}} \text { i.e. } \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{V_2}{v_1}} \\
\therefore & \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{64}{16}}=2 \\
\therefore & \lambda_2=\frac{\lambda_1}{2}
\end{array}\)
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