A) \[1:1\]
B) \[1:2\]
C) \[2:1\]
D) \[1:4\]
Correct Answer: A
Solution :
: Kinetic energy of a charged particle, \[K=\frac{1}{2}m{{\upsilon }^{2}}\] or \[\upsilon =\sqrt{\frac{2K}{m}}\] Radius of the circular path of a charged particle in a uniform magnetic field is \[r=\frac{m\upsilon }{qB}=\frac{m}{qB}\sqrt{\frac{2K}{m}}=\frac{\sqrt{2Km}}{qB}\] Since K and B are same for both the particles, \[\therefore \] \[r\propto \frac{\sqrt{m}}{q}\] \[\therefore \] \[\frac{{{r}_{p}}}{{{r}_{\propto }}}=\sqrt{\frac{{{m}_{p}}}{{{m}_{q}}}}\times \frac{{{q}_{\alpha }}}{{{q}_{p}}}\](\[\because \] a is a helium nucleus) \[=\sqrt{\frac{m}{4m}}\times \frac{2e}{e}=1\] \[{{r}_{p}}:{{r}_{\alpha }}=1:1\]
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