MCQ
A hydrogen atom makes a transition from $n = 2$ to  $n = 1$ and emits a photon. This photon strikes a doubly ionized lithium atom $(z = 3)$  in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is
  • A
    $2$
  • $4$
  • C
    $5$
  • D
    $3$

Answer

Correct option: B.
$4$
b
A hydrogen atom makes a transition from $n=2$ to $n=1$

Then wavelength

$=\operatorname{Rcz}^{2} \frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}=\operatorname{Rc}(1)^{2}\left[1-\frac{1}{4}\right]$

$\lambda=\operatorname{Rc}\left[\frac{3}{4}\right]$   ..... $(1)$

Forionized lithium

$\lambda=\operatorname{Rc}(3)^{2}\left[\frac{1}{n^{2}}\right]=\operatorname{Rc} 9\left[\frac{1}{n^{2}}\right]$    ..... $(2)$

$\operatorname{Rc}\left[\frac{3}{4}\right]=\operatorname{Rc9}\left[\frac{1}{n^{2}}\right]$

$\Rightarrow \frac{3}{4}=\frac{9}{n^{2}} \Rightarrow n=\sqrt{12}=2 \sqrt{3}$

The least quantum number must be $4$.

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