JEE Mains · Chemistry · STD 11 - 2. structure of atom
A proton and a \(Li ^{3+}\) nucleus are accelerated by the same potential. If \(\lambda_{L i}\) and \(\lambda_{P}\) denote the de Broglie wavelengths of \(Li ^{3+}\) and proton respectively, then the value of \(\frac{\lambda_{ Li }}{\lambda_{ P }}\) is \(x \times 10^{-1}\).The value of \(x\) is ............ (Rounded off to the nearest integer) (Mass of \(Li ^{3+}=8.3\) mass of proton)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\lambda=\frac{ h }{\sqrt{2 mqV }}\) \(\frac{\lambda_{ Li }}{\lambda_{ p }}=\sqrt{\frac{ m _{ p }( e ) V }{ m _{ Li }(3 e )( V )}} \quad m _{ Li }=8.3 m _{ p }\) \(\frac{\lambda_{ Li }}{\lambda_{ p }}=\sqrt{\frac{1}{8.3 \times 3}}=\frac{1}{5}=0.2=2 \times 10^{-1}\)
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