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 :

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

Tardigrade Admin · Accepted Answer

q Δ V =(1/2) m V 2 ⇒ v =√(2 q Δ V / m ) ∴ ( V 1/ V 2)=√( e / m ) (4 m / e )=2

Q. 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 :

$5 : 7$

$1 : 2$

$10 : 7$

$2 : 1$

$q Δ V = \frac{1}{2} m V^{2}$
$\Rightarrow v = \frac{2 q Δ V}{m}$
$∴ \frac{V _{1}}{V _{2}} = \frac{e}{m} \frac{4 m}{e} = 2$