1. Tardigrade
  2. Question
  3. Chemistry
  4. A proton and a Li 3+ nucleus are accelerated by the same potential. If λ Li and λ P denote the de Broglie wavelengths of Li 3+ and proton respectively, then the value of (λ Li /λ p ) is x × 10- 1. The value of x is (Rounded off to the nearest integer) (Mass of Li 3+=8.3 mass of proton)

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Q. A proton and a $Li ^{3+}$ nucleus are accelerated by the same potential. If $\lambda_{ Li }$ 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)

JEE MainJEE Main 2021Structure of Atom

Solution:

$\lambda=\frac{ h }{\sqrt{2 mqV }}$

$\frac{\lambda_{ Li }}{\lambda_{ p }}=\sqrt{\frac{ m _{ p }( e ) V }{ m _{ Li }(3 e )( V )}} $

$m _{ Li }=8.3 m _{ p }$

$\frac{\lambda_{ Li }}{\lambda_{ p }}=\sqrt{\frac{1}{8.3 \times 3}}=\frac{1}{5}=0.2$

$=2 \times 10^{-1}$