A) \[1:3\]
B) \[1:\sqrt{2}\]
C) \[1:2\]
D) \[1:\sqrt{3}\]
Correct Answer: B
Solution :
We know that \[r=\frac{mv}{Bq}=\frac{\sqrt{2mqV}}{Bq}=\frac{1}{B}\sqrt{\frac{2mV}{q}}\Rightarrow r\propto \sqrt{\frac{m}{q}}\] Given\[\frac{{{m}_{p}}}{{{m}_{\alpha }}}=\frac{1}{4};\frac{{{q}_{p}}}{{{q}_{\alpha }}}=\frac{1}{2}\] \[\frac{{{r}_{p}}}{{{r}_{\alpha }}}=\sqrt{\frac{{{m}_{p}}{{q}_{\alpha }}}{{{q}_{p}}{{m}_{\alpha }}}}=\sqrt{\left( \frac{1}{4} \right)\left( \frac{2}{1} \right)}=\frac{1}{\sqrt{2}}\]
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