A proton, a deutron and `alpha`-particle, whose kinetic energies are same, enter perpendicularly a uniform magnetic field. Compare the radii of their circualr paths.

Options

A. `1:1:sqrt2`
B. `sqrt2:1:1`
C. `1:sqrt2:1`
D. `1:2:sqrt2`

Answer

C

Explanation

`because r=(sqrt(2mE))/(Bq), therefore r prop (sqrtm)/(q)`
`"Hence, "r_(p): r_(d): r_(alpha)=(sqrt(m_(p)))/(q_(p)):(sqrt(m_(d)))/(q_(d)):(sqrt(m_(alpha)))/(q_(alpha))`
`=(sqrtm)/(e):(sqrt(2m))/(e):(sqrt(4m))/(2e)=1:sqrt2:1`