1.

A proton, a deuteron and an alpha-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If r_p, r_d and r_alpha denote respectively the radii of the trajectoriesof these particles then :-

Answer»

`r_alpha= r_d gt r_p`
`r_alpha =r_d = r_p`
`r_alpha lt r_d lt r_p`
`r_alpha = r_p lt r_d`

Solution :Radius of the circular path of charged PARTICLE in a magnetic field is GIVEN by :
`r=(MV)/(Bq)=sqrt(2mK)/(Bq)` ( `because` Kinetic ENERGY , `K=1/2mv^2` )
For the same value of K and B ,
`r PROP sqrtm/q`
`therefore r_p : r_d : r_alpha =sqrtm_p/q_p : sqrtm_d/q_d :sqrtm_alpha/q_alpha`
`=sqrtm/e :sqrt(2m)/e : sqrt(4m)/(2e)=1:sqrt2:1`
or `r_alpha = r_p lt r_d`


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