InterviewSolution
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InterviewSolution
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A particle A with a mass `m_(A)` is moving with a velocity v and hits a particle B (mass `m_(B)`) at rest (one dimensional motion). Find the change the de-Broglie wavelength of the particle A. Treat the collision as elastic. |
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Answer» As collision is elastic, hence laws of conservation of momentum and kinetic energy are obeyed. According to law of conservation of momentum `m_(A)v+m_(B)0=m_(A)v_(1)+m_(B)v_(2) or m_(A)(v-v_(1))=m_(B)v_(2).......(i)` According to law of conservation of kinetic energy `1/2m_(A)v^(2)=1/2m_(A)v_(1)^(2)+1/2m_(B)v_(2)^(2) or m_(A)(v^(2)-v_(1)^(2))=m_(B)v_(2)^(2)` or `m_(A)(v-v_(1))(v-v_(1))=m_(B)v_(2)^(2).........(ii)` Dividing (ii) by (i), we get `v+v_(1)=v_(2) or v=v_(2)-v_(1)...(iii)` Solving (i) and (iii), we get `v_(1)=((m_(A)-m_(B))/(m_(A)+m_(B)))v` and `v_(2)=((2m_(A))/(m_(A)+m_(B)))v` `lambda_("initial")=h/(m_(A)v), lambda_("final")=h/(m_(A)v_(1))=(h(m_(A)+m_(B)))/(m_(A)(m_(A)-m_(B))v)` `:. Deltalambda=lambda_("final")-lambda_("initial")=h/(m_(A)v)[((m_(A)-m_(B)))/((m_(A)-m_(B)))-1]` |
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