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