Dual Nature Of Light Question 414

Question: The ratio of the $ {\lambda_{\min }} $ in a Coolidge tube to $ {\lambda_{deBroglie}} $ of the electrons striking the target depends on accelerating potential V as

Options:

A) $ \frac{{\lambda_{\min }}}{{\lambda_{deBroglie}}}\propto \sqrt{V} $

B) $ \frac{{\lambda_{\min }}}{{\lambda_{deBroglie}}}\propto V $

C) $ \frac{{\lambda_{\min }}}{{\lambda_{deBroglie}}}\propto \frac{1}{\sqrt{V}} $

D) $ \frac{{\lambda_{\min }}}{{\lambda_{deBroglie}}}\propto \frac{1}{V} $

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Answer:

Correct Answer: C

Solution:

[c] $ {\lambda_{\min }}=\frac{hc}{eV} $ and $ {\lambda_{de-broglie}}=\frac{h}{p}=\frac{h}{\sqrt{2meV}}. $