Question

A helium ion and a Hydrogen ion are accelerated from rest through a potential difference of V to velocities of $v{H}_e$ and vH respectively. If the helium ion loses one electron, what will be the ratio of $v{H}_e$ to vH.

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

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

$\therefore \Delta V=V-0=V$
Now, $\frac{1}{2}m{v}_{ne}^2=Vm=2m+p+2m_e$
$\therefore \frac{\frac{1}{2}\times (m_p+m_e)V_{He}^2=V}{\frac{1}{2}\times (m_p+m_e)V_H^2=V}$
$\therefore \frac{V_{He}}{V_H}=\frac{1}{\sqrt{2}}$
Now if it will loss one electron still the ratio will be same
since $m_p>>>m_e$