Question

A proton and alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be:

• A. 4 Me V
• B. 0.5 MeV
• C. 1.5 MeV
• D. 1 Me V

Answer 1

Answer: (D)

The radius of circular path is $r=\frac{\sqrt{2mE}}{qB}$

So, $\frac{r_{\alpha }}{r_p}=\sqrt{\frac{m_{\alpha }{E}_{\alpha }}{m_p{E}_p}}\frac{q_p}{q_{\alpha }}$

or, $1=\sqrt{\frac{E_{\alpha }}{E_p}}$ as radius of both particles are equal and the mass of alpha particle is 4 times of proton and charge is 2 times of proton.

Thus, $E_{\alpha }=E_p=1$MeV