The highest-energy electron in a hydrogen atom is found in the orbital with the largest principal quantum number nnn, which corresponds to the electron being the least tightly bound to the nucleus. The energy levels of the hydrogen electron are quantized and given by the formula:
En=−13.6 eVn2E_n=-\frac{13.6\text{ eV}}{n^2}En=−n213.6 eV
where n=1,2,3,…n=1,2,3,\ldots n=1,2,3,… and 13.6 eV is the ionization energy of hydrogen
- The ground state (lowest energy) is at n=1n=1n=1 with energy −13.6-13.6−13.6 eV.
- As nnn increases, the energy becomes less negative, meaning the electron is higher in energy and less tightly bound.
- The highest-energy electron corresponds to the electron being at very large nnn (approaching infinity), where the energy approaches 0 eV, which is the energy of a free, unbound electron.
In summary, the highest-energy electron in a hydrogen atom is found in the orbital with the highest principal quantum number nnn, which is the outermost orbital before ionization, where the electron is almost free from the nucleus
