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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.A. `(h)/(m_(A)v)[|(m_(A)+m_(B))/(m_(A)-m_(B))|-1]`B. `(h)/(m_(B)v)[|(m_(A)+m_(B))/(m_(A)-m_(B))|-1]`C. `(h)/(m_(A)v)[|(m_(A)-m_(B))/(m_(A)+m_(B))|-1]`D. `(h)/(m_(B)v)[|(m_(A)-m_(B))/(m_(A)+m_(B))|-1]` |
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Answer» Correct Answer - A From the law of conservation of momentum `m_(A)v=m_(A)v_(B)` or `m_(A)(v-v_(A))=m_(B)v_(B)" "...(i)` `(1)/(2)m_(A)v^(2)=(1)/(2)m_(A)v_(A)^(2)+(1)/(2)m_(B)v_(B)^(2)` `m_(A)(v^(2)-V_(A)^(2))=m_(B)v_(B)^(2)` Dividing eqn. (ii) by eqn. (i), we obtain or `(v)/(v_(A))=((m_(A)+m_(B))/(m_(A)-m_(B)))" "...(iv)` Change in wavelength `Deltalambda=(lamda_(A))_("f")-(lamda_(A))=(h)/(m_(A)v_(A))-(h)/(m_(A)v)` or `Deltalamda=(h)/(m_(A)v)[(v)/(v_(A))-1]" "...(v)` From eqn. (iv) and (v). `Deltalamda=(h)/(m_(A)v)[|(m_(A)+m_(B))/(m_(A)-m_(B))|-1]` |
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