Question

A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of $\alpha -$particle (mass = 4m and charge = + 2e), so that it can revolve in the path of same radius

• A. 1 MeV
• B. 4 MeV
• C. 2 MeV
• D. 0.5 MeV

Answer 1

Answer: (A)

1 MeV

Answer 2

$K \propto \frac { q ^ { 2 } } { m }$ ⇒ $\frac { K _ { p } } { K _ { \alpha } } = \left( \frac { q _ { p } } { q _ { \alpha } } \right) ^ { 2 } \times \frac { m _ { \alpha } } { m _ { p } }$

⇒ $\frac { 1 } { K _ { \alpha } } = \left( \frac { q _ { p } } { 2 q _ { p } } \right) ^ { 2 } \times \frac { 4 m _ { p } } { m _ { p } } = 1$ ⇒ .