Quantum numbers are really important for understanding how atoms are set up, especially how electrons are organized in layers around the nucleus, which is the center of the atom. There are four main types of quantum numbers:

1. Principal Quantum Number ($n$):

   • This number tells us the main energy level or layer where an electron is found.
   • For example, if $n = 1$, the electron is in the first layer. If $n = 2$, it’s in the second layer, and so on.

2. Azimuthal Quantum Number ($l$):

   • This number has to do with the shape of the space where we find the electron.
   • It can have values from $0$ up to $n - 1$. For example, if $n = 2$, $l$ can be $0$ (which is called an s orbital) or $1$ (this is known as a p orbital).

3. Magnetic Quantum Number ($m_l$):

   • This number shows how the orbital is oriented or positioned in space within a subshell.
   • For a p orbital ($l = 1$), the possible values for $m_l$ are $-1, 0, 1$.

4. Spin Quantum Number ($m_s$):

   • This describes how the electron spins.
   • The spin can be either $+\frac{1}{2}$ or $-\frac{1}{2}$.

When we put these quantum numbers together, we can figure out the electronic arrangement of an atom. This means we can see how the electrons are set up in the shells.

For example, oxygen has the electron arrangement written as $1s^2 2s^2 2p^4$. This notation shows how these quantum numbers work together to explain where the electrons are and how they behave.