Practicing Success

Target Exam

CUET

Subject

Physics

Chapter

Atoms

Question:

The third line of Balmer series of an ion equivalent to hydrogen atom has wavelength of 108.5 nm. The ground state energy of an electron of this ion will be

Options:

3.4 eV

13.6 eV

54.4 eV

122.4 eV

Correct Answer:

54.4 eV

Explanation:

For third line of Balmer series $n_1=2$, $n_2=5$

∴  $\frac{1}{\lambda}=R Z^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$ gives $Z^2=\frac{n_1^2 n_2^2}{\left(n_2^2-n_1^2\right) \lambda R}$

On putting values $Z=2$

From $E=-\frac{13.6 Z^2}{n^2}=\frac{-13.6(2)^2}{(1)^2}=-54.4 eV$