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Energy of an electron in a system can be calculated as
$E_{n} = \frac{- 2 .18 \times 10^{- 18} Z^{2}}{n^{2}}$
Which of the following correctly states the relationship between the n = 2 level of He+ atom (Z = 2) and n = 2 level of Li²⁺ ion (Z = 3)?

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$E_{{He}^{+}} = \frac{9}{4} E_{{Li}^{2 +}}$

$E_{{He}^{+}} = \frac{4}{9} E_{{Li}^{2 +}}$

$E_{{He}^{+}} = \frac{9}{2} E_{{Li}^{2 +}}$

$E_{{He}^{+}} = \frac{2}{9} E_{{Li}^{2 +}}$

answer is B.

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Detailed Solution

$\begin{array}{l} E_{{He}^{+}} = \frac{K (2)^{2}}{(2)^{2}} = K \\ E_{{Li}^{2 +}} = \frac{K (3)^{2}}{(2)^{2}} = \frac{9}{4} K \\ \Rightarrow E_{{He}^{+}} = \frac{4}{9} E_{{Li}^{2 +}} \end{array}$

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