A particle A with a mass mA is moving with

Question:

A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.

Solution:

According to the law of conservation of momentum,

mAv + mB0 = mAv1 + mBv2

mA(v-v1) = mBv2

1/2 mAv2 = 1/2 mAv12 + 1/2mBv22

mA(v-v1)(v+v1) = mBv22

v1 = (mA-mB/mA+mB)v

v2 = (2mA/mA+mB)v

λinitial = h/mAv

λfinal = h/mAv1

∆λ = λfinal – λinitial = h/mAv(mA+mB/mA-mB)-1

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