A) \[{{R}_{d}}=\sqrt{2}\,{{R}_{p}}\]
B) \[{{R}_{d}}={{R}_{p}}/\sqrt{2}\]
C) \[{{R}_{d}}={{R}_{p}}\]
D) \[{{R}_{d}}=2{{R}_{p}}\]
Correct Answer: A
Solution :
\[\frac{m{{v}^{2}}}{R}=qvB\]. For proton \[{{R}_{p}}=\frac{mv}{qB}=\frac{\sqrt{2{{m}_{p}}E}}{qB}\] and for deutron \[{{R}_{d}}=\frac{\sqrt{2{{m}_{d}}E}}{qB}\] \[\Rightarrow \,\ \frac{{{R}_{d}}}{{{R}_{p}}}=\sqrt{\frac{{{m}_{d}}}{{{m}_{p}}}}=\sqrt{2}\Rightarrow {{R}_{d}}=\sqrt{2}{{R}_{p}}\]
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