A proton and helium nucleus are shot into a magnetic field at right angles to the field with same kinetic energy. Then the ratio of their radii is

Question

A proton and helium nucleus are shot into a magnetic field at right angles to the field with same kinetic energy. Then the ratio of their radii is (A) 1: 1 (B) 1: 2 (C) 2: 1 (D) 1: 4

Tardigrade Admin · Accepted Answer

The radius of the circular path, of a charges particle in magnetic field

r = \frac{m v}{qB} = \frac{2 m E}{qB}

Here, kinetic energy for proton and helium is same and both are moving in the same magnetic field

∴ r \propto \frac{m}{q}

So,

\frac{r _{p}}{r _{e}} = \frac{\frac{m _{p}}{q _{p}}}{\frac{m _{He}}{q _{He}}} = \frac{m _{p}}{m _{He}} \times \frac{q _{He}}{q _{p}} = \frac{m}{4 m} \cdot \frac{2 q}{q} = \frac{1}{1}

Q. A proton and helium nucleus are shot into a magnetic field at right angles to the field with same kinetic energy. Then the ratio of their radii is

1 : 1

1 : 2

2 : 1

1 : 4