An electron a, proton and an alpha particle having the same kinetic energy moving in circular orbits of radii `r_(e), r_(p),r_(alpha` respectively in a uniform magnetic field B. The relation between `r_(e), r_(p),r_(alpha)` is

Options

A. `r_(e)lt r_(p) lt r_(alpha)`
B. `r_(e)lt r_(alpha) lt r_(p)`
C. `r_(e)gt r_(p) gt r_(e)gt r_(alpha)`
D. `r_(e)lt r_(p) lt r_(e)lt r_(alpha)`

Explanation

For a charged particle moving in a circular obrit,
`r= (sqrt(2mB))/(qB)` [ r= radius of the circular orbit, E= kinetic energy of the particle]
`:.(r_(alpha))/(r_p) = (sqrt(2m_(alpha)))/(q_(alpha))xx(q_(p))/(sqrt(2m_(p)))=1` [ since `m_(alpha)= m_(p) and q_(alpha)=2q_(p)]`
`:. r_(alpha)=r_(p)`
Now, since mass of electron is less than the mass of both proton and `alpha`-particle `r_(e)` will be less than both `r_(p) and r_(alpha)`
`:.r_(e) lt r_(p), r_(e) lt r_(alpha)`
The option d is correct.