MCQ
The wave no. of the first line of Balmer series of $H$ atom is $15200\ cm^{-1}$ . What is wave number of the first line of Lyman series of $Li^{2+}$ ................ $\mathrm{cm}^{-1}$
- A$456200$
- B$136800$
- ✓$738720$
- D$152000$
✓
Answer
Correct option: C.
$738720$
c
$\frac{15200}{\frac{1}{\lambda}}=\frac{R_{H} \times\left[\frac{1}{4}-\frac{1}{9}\right]}{R_{H} \times 9\left[\frac{1}{1}-\frac{1}{4}\right]}=\frac{\frac{5}{9 \times 4}}{\frac{9 \times 3}{4}}=\frac{5}{9 \times 9 \times 3}$
$\frac{15200}{\frac{1}{\lambda}}=\frac{R_{H} \times\left[\frac{1}{4}-\frac{1}{9}\right]}{R_{H} \times 9\left[\frac{1}{1}-\frac{1}{4}\right]}=\frac{\frac{5}{9 \times 4}}{\frac{9 \times 3}{4}}=\frac{5}{9 \times 9 \times 3}$
$\frac{1}{\lambda}=\frac{15200}{5} \times 9 \times 9 \times 3=738720$
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