A) \[{{r}_{e}}={{r}_{p}}\]
B) \[{{r}_{e}}<{{r}_{p}}\]
C) \[{{r}_{e}}>{{r}_{p}}\]
D) \[{{r}_{e}}\] may be less than or greater than \[{{r}_{p}}\] depending on the direction of the magnetic field
Correct Answer: B
Solution :
\[r=\frac{\sqrt{2mK}}{qB}i.e.\ \ r\propto \frac{\sqrt{m}}{q}\] Here kinetic energy K and B are same. \[\therefore \ \frac{{{r}_{e}}}{{{r}_{p}}}=\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\times \frac{{{q}_{p}}}{{{q}_{e}}}\Rightarrow \frac{{{r}_{e}}}{{{r}_{p}}}=\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\ \ (\because \ {{q}_{e}}={{q}_{p}})\] Since me < mp, therefore re < rp
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