A) 1 : 4
B) 1 :\[\sqrt{2}\]
C) 1 : 1
D) 1 : 2
Correct Answer: B
Solution :
For a moving charge in a perpendicular magnetic field, \[\frac{m{{v}^{2}}}{r}=Bqv\] \[\Rightarrow \] \[r\frac{mv}{Bq}=\frac{p}{Bq}\] or \[\frac{{{r}_{p}}}{{{r}_{d}}}=\frac{{{p}_{p}}}{{{p}_{d}}}\] ?(i) (as q is same for both) Also, momentum \[p=\sqrt{2mE}\] or \[\frac{{{p}_{p}}}{{{p}_{d}}}=\sqrt{\frac{{{m}_{p}}}{{{m}_{d}}}}\] ...(ii) From Eqs. (i) and (ii), we have, \[\frac{{{r}_{p}}}{{{r}_{d}}}=\sqrt{\frac{{{m}_{p}}}{{{m}_{d}}}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}\]
You need to login to perform this action.
You will be redirected in
3 sec
