Question

Assume that the potential energy of a hydrogen atom in its ground state is zero. Then its total energy in the first excited state will be:

• A. $13.6eV$
• B. $27.2eV$
• C. $23.8eV$
• D. $10.2eV$

Answer 1

The correct option is C $23.8eV$

$-PE=2KE=2\times (+13.6)=27.2eV.$

$\therefore PE=-27.2eV$

PE with respect to ground state $=27.2eV$ which we assume to be zero.

$KE=-\frac{13.6}{n^2}eV$

For the first excited state, $n=2$

$\therefore KE=\frac{13.6}{2^2}eV=-3.4eV$

Total energy $=(27.2-3.4)eV=23.8eV$.