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 :
λAλB=13
λAλB=12
λAλB=2
λAλB=23
A
λAλB=12
B
λAλB=13
C
λAλB=2
D
λAλB=23
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Solution
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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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