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 in 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, `" "1/2m_(A)v^(2)=1/2m_(A)v_(1)^(2)+1/2m_(B)v_(2)^(2)` `implies" "m_(A)(v-v_(1))-m_(B)v_(2)` 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)` `implies" "m_(A)(v-v_(1)^(2))=m_(B)v_(2)^(2)` `implies" "m_(A)(v-v_(1))(v+v_(1))=m_(B)v_(2)` Dividing Eq. (ii) by Eq. (i) we get, `" "v+v_(1)=v_(2)orv=v_(2)-v_(1)` Solving Eqs (i) and (iii), we get `" "v_(1)=((m_(A)-m_(B))/(m_(A)+m_(B)))vand v_(2)=((2m_(A))/(m_(A)+m_(B)))v` `" "lamda_("initial")=h/(m_(A)v)` `" "lamda_("final")=h/(m_(A)v_(1))=(h(m_(A)+m_(B)))/(m_(A)(m_(A)-m_(B))v)` `" "Deltalamda=lamda_("final")-lamda_("initial")=(h)/(m_(A)v)[(m_(A)+m_(B))/(m_(A)-m_(B))-1]` |
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