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

Options

A. `r_(alpha)=r_(d)gtr_(p)`
B. `r_(alpha)=r_(d)=r_(p)`
C. `r_(alpha)ltr_(d)ltr_(p)`
D. `r_(alpha)=r_(p)ltr_(d)`

Answer

D

Explanation

Radius of the circular path of the charged particle in a magnetic field is given by:
`r=(mv)/(Bq)=(sqrt(2mK))/(Bq)`
`( :'` Kinetic energy `K=1/2mv^(2))`
For the same value of K and B
`r prop (sqrt(m))/q`
`:.r_(p):r_(d):r_(alpha)=(sqrt(m_(F)))/(q_(p)):(sqrt(m_(d)))/(q_(d)):(sqrt(m_(alpha)))/(q_(alpha))`
`=(sqrt(m))/e:(sqrt(2m))/e:(sqrt(4m))/(2e)=1:sqrt(2):1`
or `r_(alpha)=r_(p)ltr_(d)`