JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Work, Power & Energy

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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:

(A) $1 : 2$
(B) $10 : 7$
(C) $5 : 7$
(D) $2 : 1$ ✓ Correct

Answer: (D)

Solution

Accelerating a charge

q

from rest through a potential difference

V

gives it kinetic energy

q V = \frac{1}{2} m v^{2}

, so

v = 2 q V / m

, and for a fixed

V

this makes

v \propto q / m

. The hydrogen ion and the singly ionised helium atom carry the same charge, so the ratio of their speeds depends only on their masses. With the hydrogen ion near

1 u

and the helium ion near

4 u

\frac{v _{H}}{v _{H e}} = \frac{m _{H e}}{m _{H}} = \frac{4}{1} = 2

, so the final speeds are close to

2 : 1

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Single correct option

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