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

Engineering

Physics

de Broglie Hypothesis and Dual Nature

Question

A particle A of mass m and initial velocity v collides with a particle B of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λ_A to λ_B after the collision is:

$\frac{λ_{A}}{λ_{B}} = \frac{1}{3}$

$\frac{λ_{A}}{λ_{B}} = \frac{1}{2}$

$\frac{λ_{A}}{λ_{B}} = 2$

$\frac{λ_{A}}{λ_{B}} = \frac{2}{3}$

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mv = mv₁ + $\frac{m}{2} v_{2}$

$v = v_{1} + \frac{v_{2}}{2}$ ...(i)

v₂ – v₁ = v ...(ii)

after sloving $v_{1} = \frac{v}{3}, v_{2} = \frac{4 v}{3}$

$P_{A} = \frac{mv}{3}, P_{B} = \frac{m}{2} \frac{4 v}{3} = \frac{2 mv}{3}$

$\frac{λ_{A}}{λ_{B}} = \frac{b / P_{A}}{λ / P_{B}} = \frac{P_{B}}{P_{A}} = \frac{2 mv}{3} \frac{3}{mv} = 2 : 1$