Question

A proton, a deuteron and an $\alpha$ - particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths described by them is

• A. $1 : \sqrt{2} : 1$
• B. $1 : \sqrt{2} : \sqrt{2}$
• C. $\sqrt{2} : 1 :1$
• D. $\sqrt{2} : \sqrt{2} : 1$

Answer 1

Answer: (A)

$1 : \sqrt{2} : 1$

Answer 2

According to the question, magnetic field is uniform and the kinetic energy for each particle are same.
We know that,
$r = \frac{m v}{q B}=\frac{\sqrt{2 m(K . E)}}{q B}$
$I \propto \frac{m}{q}$
$I_{p}: I_{d}: I_{\alpha}= \sqrt{\frac{m}{q}}: \sqrt{\frac{2 m}{q}}: \sqrt{\frac{m}{q}}$
$= 1: \sqrt{2}: 1$