A proton, a deuteron and an o particle enter a magnetic field perpendicular to field with same velocity. What is the ratio of the radii of circular paths?

Options

A. `1:2:2`
B. `2:1:1`
C. `1:1:2`
D. `1:2:1`

Answer

A

Explanation

When a charged particles of charge q and mass m enters with velocity v perpendicular to magnetic field B,it follows a circular path whose radius is given by `r=(mv)/(Bq)`
`rprop(m)/(q)` for the same value of v and B.
`:.r_(p):r_r_(alpha)= (mp)/(qp):(md)/(qd):(m_(alpha))/(q_(alpha))`
where subscripts p, d and `alpha` represent proton , deuteron and `alpha` particles respectively.
`:.r_(p):r_r_(alpha)= (m)/(qp):(2m)/(e):(4m)/(2_(e))=1:2:2`