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JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
A particle is travelling \(4\) times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is \(2: 1,\) the mass of the particle is
- A \(\frac{1}{16}\) times the mass of \(e ^{-}\)
- B \(8\) times the mass of \(e ^{-}\)
- C \(16\) times the mass of \(e ^{-}\)
- D \(\frac{1}{8}\) times the mass of \(e ^{-}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{8}\) times the mass of \(e ^{-}\)
Step-by-step Solution
Detailed explanation
\(\lambda=\frac{ h }{ p }\) \(\frac{\lambda_{ p }}{\lambda_{ e }}=\frac{ p _{ e }}{ p _{ p }}=\frac{ m _{ e } v _{ e }}{ m _{ p } v _{ p }}\) \(2=\frac{ m _{ e }}{ m _{ p }}\left(\frac{ v _{ e }}{4 v _{ e }}\right)\) \(\therefore m _{ p }=\frac{ m _{ e }}{8}\)
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