A proton, a deuteron and an a-particle have same kinetic energies. Their velocities are in the ratio of:

Options

A. `1:sqrt2:1`
B. `1:1:sqrt2`
C. `sqrt2:1:1`
D. `1:(1)/(sqrt(2)):1`

Answer

A

Explanation

Here `r=(mv)/(Be)= sqrt((mxx mv^(2)))/(Be)=sqrt(2mE_(k))/(Be)`
Here K.E. and B are the same `:. r prop (sqrt(m))/(e)`
`:.r_(p):r_(d):r_(alpha): :sqrt(m_(p))/(e): sqrt(m_(d))/(e):sqrt(m_(alpha))/(2e)=1: sqrt(2):1`
`:.m_(d)=2m_(p) and m_(alpha)=4m_(p)`