Question

The ionization energy of hydrogen atom is $13.6eV$ . Hydrogen atoms in the ground state are excited by electromagnetic radiation of energy $12.1eV$ . How many spectral lines will be emitted by the hydrogen atoms

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

Energy required for transition of electron is given by, $\Delta E=E_{0}-E_{n}$
$\Rightarrow 12.1=13.6-E_{n}$
$\Rightarrow E_{n}=13.6-12.1=1.5$
$\Rightarrow \frac{13 . 6}{n^{2}}=1.5$
$\Rightarrow n^{2}=\frac{13 . 6}{1 . 5}=9$
$\Rightarrow n=3$
Number of spectral lines $=\frac{n \left(\right. n - 1 \left.\right)}{2}=\frac{3 \left(\right. 3 - 1 \left.\right)}{2}=3$