Question

The wave number of first line of Balmer series of hydrogen is $15200{cm}^{-1}$. The wave number of the first Balmer line of ${Li}^{2+}$ ion is:

• A. $15,200{cm}^{-1}$
• B. $60,800{cm}^{-1}$
• C. $76,000{cm}^{-1}$
• D. $1,36,800{cm}^{-1}$

Answer 1

Answer: (D)

$1,36,800{cm}^{-1}$

$\overline{\nu }\propto Z^2$

${\overline{\nu }}_{L{i}^{2+}}=\frac{Z_{L{i}^{2+}}^2}{Z_H^2}\times {\overline{\nu }}_H$
${\overline{\nu }}_{L{i}^{2+}}=\frac{3^2}{1^2}\times 15200c{m}^{-1}$

${\overline{\nu }}_{L{i}^{2+}}=1,36,800c{m}^{-1}$