A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in the uniform magnetic field. What should be the energy of an alpha particle to describe a circle of the same radius in the same field.

2 MeV

1 MeV

0.5 MeV

4 MeV

Solution

1 MeV

For space proton straight r space equals space fraction numerator square root of 2 straight m left parenthesis KE right parenthesis end root over denominator qB end fraction So straight q space proportional to space square root of straight m left parenthesis KE right parenthesis end root Hence space fraction numerator straight e over denominator 2 straight e end fraction space equals space square root of fraction numerator left parenthesis straight m subscript straight p right parenthesis left parenthesis 1 space Mev right parenthesis over denominator left parenthesis 4 straight m subscript straight p right parenthesis left parenthesis KE right parenthesis end fraction end root 1 fourth space equals fraction numerator 1 space MeV over denominator 4 KE end fraction KE space equals 1 space MeV

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