Question

A proton and an $\alpha$-particle, accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is $10cm$, then radius of $\alpha$-particle is

• A. $10cm$
• B. $10\sqrt{2}cm$
• C. $20cm$
• D. $5\sqrt{2}cm$

Answer 1

Answer: (B)

$10\sqrt{2}cm$

Radius of path $r_{time}=\frac{1}{\beta }\sqrt{\frac{2mv}{q}}$
$\therefore \frac{r_{\alpha }}{r_p}=\sqrt{\frac{m_{\alpha }}{m_p}}\sqrt{\frac{q_p}{q_{\alpha }}}$
or, $\frac{r_{\alpha }}{10}=\sqrt{\frac{4}{2}}\Rightarrow r_{\alpha }=10\sqrt{2}cm$.