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JEE Advance - Physics (2008 - Paper 1 Offline - No. 18)

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 exactly valid.
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 exactly valid.
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 exactly valid.
The quantum number n of the state finally populated in He$$^+$$ ions is :
2
3
4
5

Explanation

For H atom,

$${E_1} = - {{13.6} \over {{1^2}}} = - 13.6\,eV$$

$${E_2} = - {{13.6} \over {{2^2}}} = - 3.4\,eV$$

Energy released by H atom = E$$_2$$ $$-$$ E$$_1$$

$$ = - 3.4 - ( - 13.6) = 10.2\,eV$$

This energy will be absorbed by He atom. Thus, for He atom

$$10.2 = - 13.6 \times {2^2}\left( {{1 \over {{2^2}}} - {1 \over {{n^2}}}} \right)$$

$$0.1875 = {1 \over 4} - {1 \over {{n^2}}}$$

$${n^2} = 16$$

$$n = 4$$

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