Saved Bookmarks
| 1. |
A particle A with a mass m_(A) is moving 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. |
|
Answer» Solution :initial de-Broglie wavelength (before collision)for particle A, `lambda_(i)=(h)/(m_(A)v_(i))=(h)/(m_(A)v)`(`because v_(i)=v)`……(1) Now ,final velocity of particle A ACCORDING to formula, `v_(f)=((m_(A)-m_(B))/(m_(A)+m_(B)))v_(i)=((m_(A)-m_(B))/(m_(A)+m_(B)))v(becausev_(i)=v)` ......(2) `implies`final de-Broglie wavelength for particle A, `lambda_(f)=(h)/(m_(A)v_(f))=(h)/(m_(A))xx((m_(A)+m_(b)))/(m_(A)-m_(B)v)` .....(3) From equations (1) and (3) ,REQUIRED change is ,`lambda_(f)-lambda_(i)=(h)/(m_(A)v)((m_(A)+m_(B))/(m_(A)-m_(B))-1)` `(h)/(m_(A)v)((m_(A)+m_(B)-m_(A)+m_(B))/(m_(A)-m_(B)))` `(2hm_(B))/(m_(A)(m_(A)-m_(B))v)`. |
|