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

Correct answer: 0 λ = h 2mqV λ _ Li λ _ p = m _ p (e)V m _ Li (3e)(V) m _ Li = 8 . 3 m _ p λ _ Li λ _ p = (1)/(8 . 3 × 3) = (1)/(5) = 0 . 2 = 2 × 10 ^ - 1

JEE Main 202124 FebruaryMorning Shift

Exam: JEE Main
Year: 2021
Date: 24 February
Shift: Morning Shift
Subject: Chemistry
Chapter: Structure of Atom

JEE Main 2021 · 24 February · Morning Shift · Chemistry · Structure of Atom

A proton and a Li ^ 3 + nucleus are accelerated by the same...

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

\dfrac{{\lambda}_{Li}}{{\lambda}_{p}}

x \times {10}^{- 1}

. The value of

x

is _____ (Rounded off to the nearest integer) [Mass of

{Li}^{3 +} = 8 . 3

mass of proton]

Correct answer

Step-by-step solution

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

$\dfrac{{\lambda}_{Li}}{{\lambda}_{p}} = \sqrt{\dfrac{{m}_{p}\left(e\right)V}{{m}_{Li}\left(3e\right)\left(V\right)}}{m}_{Li} = 8 . 3{m}_{p}$

$\dfrac{{\lambda}_{Li}}{{\lambda}_{p}} = \sqrt{\dfrac{1}{8 . 3 \times 3}} = \dfrac{1}{5} = 0 . 2 = 2 \times {10}^{- 1}$

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