A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius R , assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be

Step-by-step solution

As charge on both proton and deuteron is same i.e. ' e ' Energy acquired by both, E= eV For Deuteron. Kinetic energy, 1 2 m V^2=e V [ V is the potential difference] v= 2 e V m_d But m_d=2 m Therefore, v= 2 e V 2 m = e V m Radius of path, R= m v e B Substituting value of ' v ' we get array r R= 2 m e v m e B R 2 = m e v m e B array For proton : aligned & 1 2 m V^2=e V & V= 2 e V m & Radius of path, R^ = m V e B = m 2 e V m e B & R^ = 2 R 2 [From eq. (i)] & R^ = R 2 aligned