If first excitation potential of a hydrogen-like atom is V e... | PHYSICS - THE LINE SPECTRA OF THE HYDROGEN ATOM | SolveeIt | Solveeit

Today, August 19

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

$\frac{4V}{3}$ electron volt

Explanation

Solution

First excitation energy

= Rhc $\left( \frac{1}{1^{2}}–\frac{1}{2^{2}} \right)$ = Rch × $\frac{3}{4}$

$\frac{3}{4}$ Rhc = V eV

Rch = $\frac{4V}{3}$ eV