# What are the quantum numbers for Bromine?

Jun 3, 2017

Quantum Numbers define the character of an electron in an energy specific orbital. They do not define an element.

#### Explanation:

4 Quantum Numbers define the character of an electron in an energy specific orbital.

According to the Pauli Exclusion principle, no two electrons can have the same set of 4 quantum numbers. This is significant in that elements with multiple electrons cannot have more than two in a single orbital.

Think of the set of Quantum Numbers for an electron as being a 'discrete energy window' for that electron and no other electron in the element's electron configuration can occupy the same energy window.

The 4 Quantum Numbers (QN) and what they describe are:

• Principle QN ($n$) => Defines Principal Energy Level
• Orbital QN ($l$); also known as Angular Momentum QN => Shape of Orbital
• Magnetic QN (${m}_{l}$) => Orientation of orbital in 3 dimensions
• Spin QN (${m}_{s}$) => the spin of the electron, up or down $\pm \frac{1}{2}$, respectively).

The 4 Quantum Numbers for the 'last' electron to fill a Bromine electronic configuration would be the electron in the half-filled $4 p$ orbital...

$\implies \left(n , l , {m}_{l} , {m}_{s}\right) = \left(4 , 1 , \left\{- 1 , 0 , + 1\right\} , - \frac{1}{2}\right) \implies$ represents only one of 35 electrons in the neutral Bromine atom.

We choose the set of ${m}_{l}$ because the three $4 p$ orbitals are identical and thus there are three configurations that have the same energy:

$4 {p}_{x}^{2} 4 {p}_{y}^{2} 4 {p}_{z}^{\textcolor{b l u e}{1}}$

$4 {p}_{x}^{2} 4 {p}_{y}^{\textcolor{b l u e}{1}} 4 {p}_{z}^{2}$

$4 {p}_{x}^{\textcolor{b l u e}{1}} 4 {p}_{y}^{2} 4 {p}_{z}^{2}$