He⁺ and Li²⁺ are initially in their third and second excited states respectively. The He⁺ electron falls to its second orbit and transfers that energy to Li²⁺, exciting it further. Li²⁺ then returns t

Question

He⁺ and Li²⁺ are initially in their third and second excited states respectively. The He⁺ electron falls to its second orbit and transfers that energy to Li²⁺, exciting it further. Li²⁺ then returns to ground. If the total number of observed spectral lines is K , find K /3 .

TestHub · Accepted Answer

He⁺ starts at n=4. Its 4→2 release is 13.6×4(1/2²-1/4²)=10.2 eV. Li²⁺ starts at n=3 and absorbs it: 13.6×9(1/3²-1/n²)=10.2 gives n=6. An ensemble de-exciting from n=6 can produce 6×5/2=15 spectral lines, so K/3=5. This uses the ensemble-line convention of the printed answer.

Chemistry - Atomic Structure Question with Solution | TestHub

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