JEE MAIN - Physics (2020 - 3rd September Evening Slot - No. 6)
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 :
2 : 1
1 : 2
5 : 7
10 : 7
Explanation
We know, kinetic energy K = qV
also $$K = {{{P^2}} \over {2m}}$$
$$ \therefore $$ $$qV = {{{P^2}} \over {2m}} = {{{m^2}{v^2}} \over {2m}}$$
$$V = \sqrt {{{2qv} \over m}} $$
$$V \propto \sqrt {{q \over m}} $$
$${{{V_H}} \over {{V_{He}}}} = {{\sqrt {{e \over m}} } \over {\sqrt {{e \over {4m}}} }} = {2 \over 1}$$
also $$K = {{{P^2}} \over {2m}}$$
$$ \therefore $$ $$qV = {{{P^2}} \over {2m}} = {{{m^2}{v^2}} \over {2m}}$$
$$V = \sqrt {{{2qv} \over m}} $$
$$V \propto \sqrt {{q \over m}} $$
$${{{V_H}} \over {{V_{He}}}} = {{\sqrt {{e \over m}} } \over {\sqrt {{e \over {4m}}} }} = {2 \over 1}$$
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