JEE Main 2017 · 2 Apr · Shift 1 · Physics Q24

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A particle A of mass m and initial velocity $v$ collides with a particle B of mass $\dfrac m2$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $\lambda_A$ to $\lambda_B$ after the collision is :

\dfrac{\lambda_A}{\lambda_B}=\dfrac13

\dfrac{\lambda_A}{\lambda_B}=2

\dfrac{\lambda_A}{\lambda_B}=\dfrac23

\dfrac{\lambda_A}{\lambda_B}=\dfrac12

Answer and worked solution

Official answer: B

Elastic head-on collision, $m$ on $\frac m2$ at rest:

$v_A=\dfrac{m-m/2}{3m/2}v=\dfrac v3$ , so $p_A=\dfrac{mv}3$ .
$v_B=\dfrac{2m}{3m/2}v=\dfrac{4v}3$ , so $p_B=\dfrac{2mv}3$ .

$\dfrac{\lambda_A}{\lambda_B}=\dfrac{p_B}{p_A}=2$ .

Topics:de Broglie waves Elastic and inelastic collisions

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JEE Main 2017 · 2 Apr · Shift 1, Physics question 24