A) 1 : 2
B) 1 : 4
C) 1 : 16
D) 4 : 1
Correct Answer: A
Solution :
Key Idea: The centripetal force to the two types of particles is provided by magnetic force. Alpha particles are highly ionizing form of particle radiation which have low penetration. They consist of two protons and two neutrons bound together identical to helium nucleus. Also proton is \[_{1}{{H}^{1}}\]. Hence, \[{{m}_{\alpha }}=4{{m}_{p}}\] and \[{{q}_{\alpha }}=2{{q}_{p}}\] When proton and a-particle describe circular paths then centripetal and centrifugal forces balance each other \[\frac{m{{v}^{2}}}{r}=qvB\] \[\Rightarrow \] \[\frac{{{r}_{p}}}{{{r}_{\alpha }}}=\frac{{{m}_{p}}v}{eB}\times \frac{2eB}{4{{m}_{p}}v}\] \[\frac{2{{m}_{p}}}{4{{m}_{p}}}=\frac{1}{2}\] \[\therefore \] \[{{r}_{p}}:{{r}_{\alpha }}=1:2\]
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