The electron in the n ^ th orbit of Li ^ 2+ is excited to (n+1) o… - Vidyadip

MCQ

The electron in the $n ^{\text {th }}$ orbit of $Li ^{2+}$ is excited to $(n+1)$ orbit using the radiation of energy $1.47 \times 10^{-17}\,J$ (as shown in the diagram). The value of $n$ is $....$.Given $R_H=2.18 \times 10^{-18}\,J$

A
$2$
B
$3$
✓
$1$
D
$4$

✓

Answer

Correct option: C.

$1$

c
$\Delta E = R _{ H } Z ^2\left(\frac{1}{ n _1^2}-\frac{1}{ n _2^2}\right)$

$1.47 \times 10^{-17}=2.18 \times 10^{-15} \times 9\left(\frac{1}{n^2}-\frac{1}{(n+1)^2}\right)$

$\frac{1.47}{1.96}=\frac{3}{4}=\frac{1}{n^2}-\frac{1}{(n+1)^2}$

So, $n =1$

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