Question

The wavelength of the radiation emitted by Hydrogen when compared to ${He}^{+}$ is:

• A. 2 times that of ${He}^{+}$ ion
• B. 3 times that of ${He}^{+}$ion
• C. 4 times that of ${He}^{+}$ ion
• D. same as ${He}^{+}$

Answer 1

The correct option is C 4 times that of ${He}^{+}$ ion

Rydberg's formula for hydrogen like element
$\frac{1}{\lambda }=R{Z}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
$\therefore \lambda \propto 1/Z^2$
Atomic number of $H{e}^{+}$ is double of H
Hence
${\lambda }_H=4{\lambda }_{H{e}^{+}}$