A proton and an alpha particle enter a uniform magnetic field with the same velocity and move along circular paths. The time period of the alpha particle will be:

Four times that of proton Three times that of proton Same as that of proton Two times that of proton

Two times that of proton

$ T_p = \frac{2\pi m_p}{q_p B}$ $ T_\alpha = \frac{2\pi m_\alpha}{q_\alpha B}$ $ \frac{T_\alpha}{T_p} = \frac{m_\alpha}{m_p} \frac{q_p}{q_\alpha} = 4\times \frac{1}{2} = 2$ $ T_\alpha = 2 T_p$