When an electron in a hydrogen atom makes a transition from 2^ nd… - Vidyadip

MCQ

When an electron in a hydrogen atom makes a transition from $2^{nd}$ excited state to ground state, it emits a photon of frequency $f$ . The frequency of photon emitted when an electron of $Li^{++}$ makes a transition from $1^{st}$ excited state to ground state is

✓
$\frac{{243}}{{32}}f$
B
$\frac{{81}}{{32}}f$
C
$\frac{{243}}{8}f$
D
$\frac{{27}}{8}f$

✓

Answer

Correct option: A.

$\frac{{243}}{{32}}f$

a
$\mathrm{f}=\mathrm{C} \times 1^{2}\left(\frac{1}{1^{2}}-\frac{1}{9}\right)=\frac{8}{9} \mathrm{C}$

$f=C \times 3^{2}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)=\frac{27}{4} C=\frac{27}{4} \times \frac{9 f}{8}$

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