Question

An electron is accelerated from rest by 480 V, its wavelength is $\lambda$. If accelerated by 120 V, the wavelength is:

• A. $5\lambda$
• B. $4\lambda$
• C. $2\lambda$
• D. $3\lambda$
• E. $6\lambda$

Hint:

If voltage decreases by a factor of 4, the wavelength increases by a factor of $\sqrt{4} = 2$.

Answer 1

The Correct Option is C

Step 1: Concept
The de Broglie wavelength for an accelerated electron is $\lambda \propto \frac{1}{\sqrt{V}}$.

Step 2: Analysis
$\frac{\lambda_2}{\lambda_1} = \sqrt{\frac{V_1}{V_2}}$.

Step 3: Calculation
$\frac{\lambda_2}{\lambda} = \sqrt{\frac{480}{120}} = \sqrt{4} = 2$.
$\lambda_2 = 2\lambda$. Final Answer: (C)