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JEE Advance - Physics (2008 - Paper 1 Offline - No. 19)

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 wavelength of light emitted in the visible region by He$$^+$$ ions after collisions with H atoms is
$$6.5\times10^{-7}$$ m
$$5.6\times10^{-7}$$ m
$$4.8\times10^{-7}$$ m
$$4.0\times10^{-7}$$ m

Explanation

$${{hc} \over \lambda } = {E_4} - {E_3}$$

$${{hc} \over \lambda } = - 13.68 \times {2^2}\left( {{1 \over {{4^2}}} - {1 \over {{3^2}}}} \right)$$

$${{hc} \over \lambda } = 13.6 \times {2^2}\left( {{1 \over 9} - {1 \over {16}}} \right)$$

$${{4.1356 \times {{15}^{ - 15}}\,eV.s \times 3 \times {{10}^8}\,m{s^{ - 1}}} \over 1} = 2.644$$

$$ \Rightarrow \lambda \cong 4.8\, * \,{10^{ - 7}}\,m$$

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