A proton (mass m and charge `+e`) and an `alpha`-particle (mass `4` m and charge `+2e`) are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true?

Options

A. The alpha-particle will be bent in a circular path with a small radius that for the proton
B. The radius of the path of the alpha-particle will be greater than that of the proton
C. The alpha-particle and the proton will be bent in a circular path with the same radius
D. The alpha-particle and the proton will go through the field in a staight line

Answer

C

Explanation

`r=sqrt(2mk)/(qB) i.e rpropsqrt(m)/(q)`
Here kinetic energy K and B are same.
`:. (r_p)/(r_alpha)=sqrt(m_p)/sqrt(malpha).(q_alpha)/q_p=sqrt(m_p)/sqrt(4m_p).(2q_p)/(q_p)=1`