A) 40MeV
B) 80MeV
C) 20MeV
D) 60MeV
Correct Answer: B
Solution :
Key Idea: In a cyclotron, centripetal force is provided by the magnetic field. A cyclotron accelerates charged particles with a high frequency alternating voltage. The magnetic force acting on particle with charge q and velocity v is \[F=qvB=\frac{m{{v}^{2}}}{r}=\]centripetal force Maximum energy, \[E=\frac{1}{2}\frac{{{B}^{2}}{{q}^{2}}{{r}^{2}}}{m}\] Hence, ratio of energy of deuteron and proton is \[\frac{{{E}_{d}}}{{{E}_{p}}}={{\left( \frac{{{q}_{p}}}{{{q}_{p}}} \right)}^{2}}\,\,\left( \frac{{{m}_{p}}}{{{m}_{d}}} \right)\] \[\frac{40}{{{E}_{p}}}={{\left( \frac{q}{q} \right)}^{2}}\,\,\left( \frac{m}{2\,m} \right)\] \[\therefore \] \[{{E}_{p}}=80\,\,MeV\].
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