Import Question JSON

$\text{Hint: The alpha particle has two times the charge of the proton and four times the mass of the proton.}$ $\text{Step 1: Find the formula of energy.}$ $\text{Radius in the circular path is given by,}$ $R = \frac{mv}{qB} = \frac{\sqrt{2mE}}{qB}$ $\text{And, the total energy of a moving particle in a circular orbit,}$ $E = \frac{q^2B^2R^2}{2m}$ $\text{Step 2: Find the energy of the proton.}$ $\text{For a proton entering a region of the magnetic field,}$ $E_1 = \frac{e^2B^2R^2}{2m_p} \quad \text{....(1)}$ $\text{where } m_p \text{ is the mass of proton.}$ $\text{Step 3: Find the energy of the alpha particle.}$ $\text{Similarly, for an } \alpha\text{-particle moving in a uniform magnetic field,}$ $E_2 = \frac{(2e)^2B^2R^2}{2(4m_p)} \quad \left[\because m_\alpha = 4m_p\right] \quad \text{...(2)}$ $\text{Dividing Eq. (ii) by eq. (i) we get,}$ $E_2 = E_1 = 1 \text{ MeV}$