A) \[\frac{1}{2}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\sqrt{2}\]
D) \[2\]
Correct Answer: B
Solution :
Key idea: 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 \[E=qV\] ?(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 \[\frac{\frac{1}{2}{{M}_{He}}{{\left( {{v}_{He}} \right)}^{2}}}{\frac{1}{2}{{M}_{H}}{{\left( {{v}_{H}} \right)}^{2}}}=\frac{qV}{q'V}\] \[\Rightarrow \] \[\left( \frac{{{v}_{He}}}{{{v}_{H}}} \right)_{,}^{2}=\frac{q}{q'}\left( \frac{{{M}_{H}}}{{{M}_{He}}} \right)\] \[=\frac{2}{1}\times \frac{1}{4}\] \[=\frac{1}{2}\] \[\Rightarrow \] \[\frac{{{v}_{H\,e}}}{{{v}_{H}}}=\frac{1}{\sqrt{2}}\]
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