What is the ground state of an atom? And what is the ionization energy and excitation energy of a hydrogen atom?

(N/A) The total energy of an electron in an atom is given by:
$E_{n} = -\frac{m Z^{2} e^{4}}{8 n^{2} h^{2} \epsilon_{0}^{2}}$
This simplifies to:
$E_{n} = -\frac{13.6 Z^{2}}{n^{2}} \text{ eV}$
The negative sign indicates that as the value of $n$ increases,the magnitude of the negative energy decreases,meaning the energy of the electron increases as it moves to orbits further from the nucleus.
When an electron is in the orbit closest to the nucleus $(n = 1)$,it has the lowest energy (the maximum negative value). This state is called the ground state.
For a hydrogen atom $(Z = 1, n = 1)$:
$E_{1} = -13.6 \text{ eV}$
The ionization energy is the minimum energy required to remove an electron from the ground state to infinity. For hydrogen,this is $13.6 \text{ eV}$.
Excitation energy is the energy required to move an electron from the ground state to a higher energy state. For the first excited state $(n = 2)$:
$E_{2} = -\frac{13.6}{2^{2}} = -3.4 \text{ eV}$
$\Delta E = E_{2} - E_{1} = -3.4 - (-13.6) = 10.2 \text{ eV}$