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A proton, a deuteron and an alpha- parti...

A proton, a deuteron and an `alpha`- particle having the same kinetic energy are moving in circular trajectors in a constant magnetic field. If `r_p, r_d` and `r_(alpha)` denote respectively the radii of the trajectories of these particles then

A

`r_(alpha)=r_pltr_d`

B

`r_(alpha)gtr_dgtr_p`

C

`r_(alpha)=r_dgtr_p`

D

`r_p=r_d=r_(alpha)`

Text Solution

Verified by Experts

The correct Answer is:
A
Radius of the circular path is given by
`r=(mv)/(Bq)=sqrt((2Km))/(Bq)`
Here `K` is the kinetic energy to the particle,
Therefore, `rpropsqrtm/q` if `K` and `B` are same
`r_p:r_d=r_(alpha)=sqrt1/1:sqrt2/1:sqrt4/1=1:sqrt2:1`
Hence, `r_(alpha)=r_pltr_d`
`:.` correct option is a.
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