Given that the binding energy of the hydrogen atom in its ground state is $- 13.6 \mathrm { eV }$, what is the energy when it is in the $n = 5$ state?
A) $- 0.544 \mathrm { eV }$
B) $2.72 \mathrm { eV }$
C) $- 2.72 \mathrm { eV }$
D) $0.544 \mathrm { eV }$

Question

Quizplus · Accepted Answer

The energy levels of a hydrogen atom can be calculated using the formula $E_n = \frac{E_1}{n^2}$, where $E_1$ is the energy of the ground state ($n=1$), and $n$ is the principal quantum number of the state in question. Given $E_1 = -13.6 \, \text{eV}$ for the ground state, the energy at $n=5$ is $E_5 = \frac{-13.6}{5^2} = \frac{-13.6}{25} = -0.544 \, \text{eV}$.

Given That the Binding Energy of the Hydrogen Atom in Its