In a mixture of `H-He^(+)` gas (`He^(+)` is singly ionized `He` atom), `H` atoms and `He^(+)` ions are excited to their respective first excited state

Monjur Alahi

In a mixture of `H-He^(+)` gas (`He^(+)` is singly ionized `He` atom), `H` atoms and `He^(+)` ions are excited to their respective first excited states. Subsequently, `H` atoms transfer their total excitation energy to `He^(+)` ions (by collisions). Assume that the Bohr model of atom is exctly valid.
The ratio of the kinetic energy of the `n=2` electron for the `H` atom to that of `He^(+)` ion is:
A. `1//4`
B. `1//2`
C. `1`
D. `2`


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Salim Ahmed Kawsar

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Correct Answer - A
Ratio of kinetic energy `K_(1)/K_(2)=((Z_(1)//n_(1))^(2))/((Z_(2)//n_(2))^(2))`
Since `n_(1)=n_(2)=2` & `Z_(1)=1`
for `H, Z_(2)=2` for `He^(+) implies K_(1)/K_(2)=1/4`

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