Hydrogen ion and singly ionized helium atom are accelerated,

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:

  1. $5: 7$

  2. $1: 2$

  3. $10: 7$

  4. $2: 1$


Correct Option: , 4

Solution:

$\mathrm{q} \Delta \mathrm{V}=\frac{1}{2} \mathrm{mV}^{2} \Rightarrow \mathrm{v}=\sqrt{\frac{2 \mathrm{q} \Delta \mathrm{V}}{\mathrm{m}}}$

$\therefore \frac{V_{1}}{V_{2}}=\sqrt{\frac{e}{m} \frac{4 m}{e}}=2$

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