The electron in the n th orbit of Li 2 + is excited to ( n + 1 ) orbit using the radiation of energy 1 . 47 × 10 - 17 J (as shown in the diagram). The value of n is ___________ Given : R H = 2 . 18 ×

Question

The electron in the n th orbit of Li 2 + is excited to ( n + 1 ) orbit using the radiation of energy 1 . 47 × 10 - 17 J (as shown in the diagram). The value of n is ___________ Given : R H = 2 . 18 × 10 - 18 J

TestHub · Accepted Answer

The difference energy between two energy levels is

$∆ E = 2.18 \times 10^{- 18} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] J$

$1.47 \times 10^{- 17} = 2.18 \times 10^{- 18} \times (9) (\frac{1}{(n)^{2}} - \frac{1}{(n + 1)^{2}})$

$0.749 = \frac{1}{n^{2}} - \frac{1}{(n + 1)^{2}}$

$n = 1$

Hence, the transition is taking place between $1 \overset{}{\to} 2$ , and it comes under Lymann series.

If we take $0.749 ≃ 0.75 = \frac{3}{4}$

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