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  • The excitation energy of a hydrogen-like ion in its first excited state is  

The excitation energy of a hydrogen-like ion in its first excited state is 40.8 \mathrm{eV}. The energy needed to remove the electron from the ion.

Option: 1

60 \mathrm{ev}


Option: 2

50 \mathrm{ev}


Option: 3

50.4 \mathrm{ev}


Option: 4

54.4 \mathrm{ev}


Answers (1)

best_answer

The expiation energy of first excited stale
\mathrm{ \begin{aligned} & E=\operatorname{Rhcz^{2}}\left[\frac{1}{1^2}-\frac{1}{2^2}\right] \\ & E=(13.6 \mathrm{ev}) \times 2^2 \times \frac{3}{4} \\ & \text { if } z=2, E=13.6 \times 4 \times \frac{3}{4}=40.8 \mathrm{eV} \\ & \end{aligned} }
thew ground state -
\mathrm{ \begin{aligned} & E=-\frac{R h c z^2}{1^2} \\ & E=-4 \times(13.6) \mathrm{eV} \\ & E=-54.4 \mathrm{eV} \end{aligned} }
Thus \mathrm{54.4 \mathrm{er} } is required to remove the electron from the ion.

Posted by

Ajit Kumar Dubey

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