Question

If the first excitation potential of a hydrogen-like atom is ${}^{\prime }{V}^{\prime }$ 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

The correct option is C $\frac{4V}{3}$ electron volt

First excitation potential of hydrogen atom ($Z=1$) is $E_2-E_1$
which is, $I.E-\frac{I.E}{4}=\frac{3}{4}I.E$
Given, this is equal to $V$.
$\Rightarrow \frac{3}{4}I.E=V\Rightarrow I.E=\frac{4V}{3}$