The hydrogen atom was initially viewed as an electron orbiting a proton. However based on electomagnetic theory this model is not practical because the atom would have an extremely short life. Bohr proposed a model of a hydrogen atom in which the electron has a number of stable orbits with set angular momentum in multiples of h / (2.p ). i.e. electrons can only occupy orbits with angular momentum of n. h / (2.p )....
h = plank constant and n = 1, 2, 3.... i.e the quantum number of the orbit.
If r₁ is the smallest radius ( 5.3 x 10 ^-11 m ) and n = the quantum number of the orbit the orbit radius =

r _n = n ² r ₁     n = 1, 2, 3...

Note : 1 eV (Electronvolt = 1,6 x 10^-19 Joules

The total energy of a hydrogen atom whose electron is in the nth orbit

E _n = E ₁ / n ²     n = 1, 2, 3... .... ( E ₁ = -13.6 eV = -2.18 x 10^-18 J.)

These permitted energies of an atom are called energy levels.   The energy levels are all negative and as a result the electron does not have enough energy to escape from the atom.   As n increases E_n approaches 0 , at this level the electron is no longer bound to the proton and the atom ceases to exist.    The work input to remove an electron from an atom in its ground state is called the ionization energy; for hydrogen the ionization energy is 13.6 eV.

When a gas or vapor is excited by the passage of an electric current, light is given off is certain specific wavelengths.  Each element has characteristic emission line spectrum.   The wavelengths in this spectrum fall into fixed series with member wavelengths related by simple formula.

When white light is shone through a cool gas or vapor, light of specific wavelengths is absorbed.  The resulting absorption spectrum correspond to a number of the wavelengths in the emission spectrum of the element.

Line spectra result from the change in energy levels in the atom.   An atom in an excited state can only remain in this state for a very short time before dropping to a lower state.   The difference in energy appears as a photon of frequency f.

E _initial - E_final = h . f

In the Bohr model of the atom one quantum number is needed, in the quantum theory four quantum numbers are used.   This theory works for atoms with numerous electrons as well as for the hydrogen atom.   The quantum numbers are identified below

The energy levels possible are mainly determined by n and only to a low extent by l and m _l.   For the hydrogen atom the energy levels are the same as for the Bohr atom. Every electron behaves as though it is a spinning charge sphere.  The amount of spin is fixed but there are two possible directions that the angular momentum vector can point in the magnetic field : "up" (m_s= + 1 / 2) and "down" (m_s= - 1 / 2).

if n = 3 then l = 0, 1, 2

The maximum number of electrons in the M (n= 3)shell are 18

Additional Notes on atoms, Molecules, crystals etc
A crude periodic table + table showing atomic propeties of elements