Question:
Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :
Correct Option: , 3
Solution:
(3) According to work energy theorem, gain in kinetic energy is equal to work done in displacement of charge.
$\therefore \quad \frac{1}{2} m v^{2}=q \Delta V$
Here, $\Delta V=$ potential difference between two positions of charge $q$.
For same $q$ and $\Delta V$.
$v \propto \frac{1}{\sqrt{m}}$
Mass of hydrogen ion $\mathrm{m}_{\mathrm{H}}=1$
Mass of helium ion $\mathrm{m}_{\mathrm{He}}=4$
$\therefore \quad \frac{v_{\mathrm{H}}}{v_{\mathrm{He}}}=\sqrt{\frac{4}{1}}=2: 1$