JEE Main On 08 April 2018 Question 11
Question: An electron, a proton and an alpha particle having the same kinetic energy are 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: [JEE Main Online 08-04-2018]
Options:
A) $ r _{e}<r _{p}<{r _{\alpha }} $
B) $ r _{e}<{r _{\alpha }}<r _{p} $
C) $ r _{e}>r _{p}={r _{\alpha }} $
D) $ r _{e}<r _{p}={r _{\alpha }} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ r=\frac{mv}{Bq}=\frac{\sqrt{2mk}}{Bq} $
$ \frac{r _{p}}{r _{e}}=\frac{\sqrt{m _{p}}}{\sqrt{m _{e}}} $
$ m _{p}>m _{e} $ $ r _{p}>r _{e} $
$ \frac{r _{p}}{{r _{\alpha }}}=\frac{\sqrt{m _{p}}}{q _{p}}\frac{2q _{p}}{\sqrt{4m _{p}}}=1 $
$ r _{p}={r _{\alpha }} $
