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Question: The wave number of electromagnetic radiation emitted during the transition of electron in between tw...

The wave number of electromagnetic radiation emitted during the transition of electron in between two levels of Li2+ ion having sum of the principal quantum numbers 4 and difference is 2, will be : (RH = Rydberg constant)

A

3.5 RH

B

4 RH

C

8 RH

D

89\frac{8}{9} RH

Answer

8 RH

Explanation

Solution

 n1+n2=4n1+n2=2}\left. \ \begin{aligned} & n_{1} + n_{2} = 4 \\ & n_{1} + n_{2} = 2 \end{aligned} \right\} so n1 = 3 and n2 = 1.

vˉ=R(3)2{1(1)2−1(3)2}=8R.\bar{\mathbf{v}}\mathbf{= R}\left( \mathbf{3} \right)^{\mathbf{2}}\left\{ \frac{\mathbf{1}}{\left( \mathbf{1} \right)^{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{\left( \mathbf{3} \right)^{\mathbf{2}}} \right\}\mathbf{= 8R.}