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Question

A particle A of mass m and initial velocity v collides with a particle B of mass m2 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 :
  1. λAλB=13
  2. λAλB=12
  3. λAλB=2
  4. λAλB=23

A
λAλB=12
B
λAλB=13
C
λAλB=2
D
λAλB=23
Solution
Verified by Toppr

From conservation of linear momentum, mv=mvB+m2vB

v=vA+vB2

Also v2=v2a+v2B2

(vA+vB2)2=v2A+(vB2)2

vAvB=vB4

vB=4vA and mB=mA2

PA=mAvA

PB=mA2×4vA=2PA

λAλB=PBPA=2PAPA=2

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