Question

A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

• A. $1 : \sqrt2 : \sqrt2$
• B. $1 : 1 : \sqrt2$
• C. $\sqrt2 : 1 : 1$
• D. $1 : \sqrt2 : 1$

Answer 1

Answer: (D)

$1 : \sqrt2 : 1$

Answer 2

∴ $r = \frac{mv}{qB}$

= $\frac{\sqrt{2m(KE)}}{qB}$

$r_1: r_2: r_3 = \frac{\sqrt m_1}{q_1} : \frac{\sqrt m_2}{q_2} : \frac{\sqrt m_3}{q_3}$

= $\frac{\sqrt 1}{1}:\frac{\sqrt 2}{1}:\frac{\sqrt 4}{2}$

= $1: \sqrt2 : 1$