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What is the exact ratio of the de-Broglie wavelengths for identical electrons accelerated from rest Atomic Structure Chemistry Question

Question

What is the exact ratio of the de-Broglie wavelengths for identical electrons accelerated from rest through potential differences of $200 \text{ volts}$ and $50 \text{ volts}$ respectively?

Answer: C

💡 Solution & Explanation

For a charged particle, wavelength $\lambda \propto 1/\sqrt{V}$. The ratio $\lambda_1 / \lambda_2 = \sqrt{V_2 / V_1} = \sqrt{50 / 200} = \sqrt{1/4} = 1/2$. Thus, the ratio is $1 : 2$.

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