Question

A proton and an $\alpha -$particle are accelerated through the same potential. The ratio of their velocities is

• A. 1:2
• B. 1:4
• C. 1:1
• D. $\sqrt{2}:1$

Answer 1

The correct option is D $\sqrt{2}:1$

Charge on proton $=\alpha$
Charge on $\alpha$-particle = $2\alpha$
Mass of proton $=\beta$
Mass of $\alpha$-particle $=4\beta$
Kinetic energy of proton,
$\frac{1}{2}\times \beta V_p^2=\alpha V$
$V_p=\sqrt{\frac{2\alpha V}{\beta }}$

And Kinetic energy of $\alpha$-particle,
$\frac{1}{2}\times 4\beta \times V_{\alpha }^2=2\alpha V$
$\Rightarrow V_{\alpha }=\sqrt{\frac{\alpha V}{\beta }}$
So,
Ratio of $V_p:V_{\alpha }=\sqrt{2}:1$