Question

A deuteron and an alpha particle, having equal kinetic energy , enter perpendicular into a magnetic field. Let $r_d$ and $r_{\alpha }$ be their respective radii of circular path. The value of $\frac{r_d}{r_{\alpha }}$ is equal to :

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

Answer 1

The correct option is A $\sqrt{2}$

We know that,

$r=\frac{mv}{qB}=\frac{\sqrt{2mKE}}{qB}$

So,

$\frac{r_d}{r_{\alpha }}=\sqrt{\frac{m_d}{m_{\alpha }}}\times \frac{q_{\alpha }}{q_d}$

$\Rightarrow \frac{r_d}{r_{\alpha }}=\sqrt{\frac{2}{4}}\times \frac{2}{1}=\sqrt{2}$

Hence, option $\left(B\right)$ is the correct answer.