Question

The energy of a hydrogen atom in its ground state is $-13.6eV$. The energy of the level corresponding to the quantum number $n=5$ is :

• A. $-5.40eV$
• B. $-0.54eV$
• C. $-8.5eV$
• D. $-2.2eV$

Answer 1

The correct option is B $-0.54eV$

The energy of the hydrogen atom in $n$th state is given by

$E_n=\frac{-13.6}{\left(n^2\right)}eV$

Here, $n=5$

$\therefore E=\frac{-13.6}{{\left(5\right)}^2}eV=-0.54eV$