A thin beam of charged particles in incident normally on the boundry of a region containing a uniform magnetic field as shown.The beam comprise of mono energetic `alpha` and `beta(-)` particles, each possessing a kinetic energy `T`.Neglecting interaction between particles of the beam, find the separation between the points on line `PQ` where the `alpha` and `beta` particles emerge out of the magnetic field.(express your answer in terms of `T,B,alpha(2e,m_(alpha)) & beta^(-)(-e,m_(e))`,where all terms have their usual meanings.)

Answer

`(2sqrt2T)/(eB){sqrtm_(alpha)/2+sqrtm_(e)}`

Explanation

`(mv^(2))/r=qVB rArrr=(mv)/(qB)=sqrt(2mT)/(qB)`
`therefore` Separation betweeen `alpha & beta` particle
`=2(r_(alpha)+r_(beta))=2{sqrt(2m_(alpha)T)/((2e)B)+sqrt(2m_(e)T)/(eB)}`
`(2sqrt(2T))/(eB)={sqrtm_(alpha)/2+sqrt(m_(e))}`
`(2sqrt(2T))/(eB)={sqrtm_(alpha)/2+sqrt(m_(e))}`