Question

If first excitation potential of a hydrogen-like atom is $V$ electron volt, then the ionization energy of this atom will be

• A. $V$ electron volt
• B. $\frac{3V}{4}$ electron volt
• C. $\frac{4V}{3}$ electron volt
• D. Cannot be calculated by given information

Answer 1

Answer: (C)

First excitation energy $=\text{Rhc}\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\text{Rhc}\frac{3}{4}$
$\therefore \frac{3}{4}\text{Rhc}=\text{V}\text{ eV}$
$\therefore \text{Rhc}=\frac{4\text{V}}{3}\text{eV}$