A proton, a deuteron and an `alpha`-particle with the same KE enter a region of uniform magnetic field, moving at right angles to B. What is the ratio of the radii of their circular paths ?

Options

A. `1:sqrt(2):1`
B. `1:sqrt(2):sqrt(2)`
C. `sqrt(2):1:`
D. `sqrt(2):sqrt(2):1`

Answer

A

Explanation

If a magnetic field is perpendicualr to velocity of particle
`(mv^(2))/(r )=BqV` or `r=(mv)/(Bq)` and `E_(k)=1/2 mv^(2)`
`mv=sqrt(2xE_(k))`
So `r=sqrt(2xE_(k))/(Bq)` or `r prop sqrt(m)/(q)` for same value of `E_(k)` and B
`r_(p):r_(d):r_(alpha)=sqrt(m)/(i):sqrt(2m)/(i):sqrt(4x)/(i) rarr 1 : sqrt(2):1`