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Question:

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 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 :

λA/λB=13

λA/λB=12

λA/λB=2

λA/λB=23

Solution:

From conservation of linear momentum, mv = mvB + (m/2)vB
v = vA + vB/2
Also v^2 = vA^2 + vB^2
(vA + vB/2)^2 = vA^2 + (vB/2)^2
vAvB = vB^2/4
vB = 4vA
and mB = mA/2
P_A = mAvA
P_B = (mA/2) × 4vA = 2P_A
λA/λB = P_B/P_A = 2P_A/P_A = 2