Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of helium and the hydrogen ions are:

Question

Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of helium and the hydrogen ions are: (A)  (1/2)  (B)  (1/√2)  (C)  √2  (D)  2

Tardigrade Admin · Accepted Answer

Mass of helium is four times of hydrogen atom.
When a voltage (potential drop)

V

is applied then energy of ion with charge

q

is

E = q V ... (1)

Also a particle of mass

m

moving with velocity

v

,
has kinetic energy is

K = \frac{1}{2} m v^{2} .... (2)

From Eqs. (1) and (2), we have

\frac{\frac{1}{2} M _{He} ( v _{He} ) ^{2}}{\frac{1}{2} M _{H} ( v _{H} ) ^{2}} = \frac{q V}{q ^{'} V}

\Rightarrow (\frac{v _{He}}{v _{H}})^{2} = \frac{q}{q ^{'}} (\frac{M _{H}}{M _{He}})

= \frac{2}{1} \times \frac{1}{4} = \frac{1}{2}

\Rightarrow \frac{v _{H} e}{v _{H}} = \frac{1}{2}

Q. Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of helium and the hydrogen ions are:

$\frac{1}{2}$

$\frac{1}{2}$

$2$

$2$

Q. Doubly ionised helium atoms and hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of helium and the hydrogen ions are:

21​

2​1​

2​

2

$\frac{1}{2}$

$\frac{1}{2}$

$2$

$2$