A) \[1\,\,MeV\]
B) \[4\,\,MeV\]
C) \[2\,\,MeV\]
D) \[0.5\,\,MeV\]
Correct Answer: A
Solution :
\[r=\frac{mv}{qB}\] \[\Rightarrow \] \[{{r}^{2}}=\frac{{{m}^{2}}{{v}^{2}}}{{{q}^{2}}{{B}^{2}}}\] In terms of energy, above equation can be written as \[{{r}^{2}}=\frac{2m\times (1/2m{{v}^{2}})}{{{q}^{2}}{{B}^{2}}}=\frac{2mE}{{{q}^{2}}{{B}^{2}}}\] Here \[r\] and \[B\]are same, hence \[\frac{{{m}_{1}}{{E}_{1}}}{{{q}_{1}}^{2}}=\frac{{{m}_{2}}{{E}_{2}}}{{{q}_{2}}^{2}}\] \[\Rightarrow \] \[\frac{m\times 1}{{{e}^{2}}}=\frac{3m\times {{E}_{2}}}{4{{e}^{2}}}\] \[\therefore \] \[{{E}_{2}}=1MeV\]
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