# The Guide to Finding Electrons – Quantum Numbers

The Quantum Numbers are a set of values which describe the shape, size, and orientation of atomic orbitals. We have different four quantum numbers which include the Principal Quantum Number, the Azimuthal Quantum Number, Magnetic Quantum Number and the Spin Quantum Number. The four quantum numbers together give us the address and other properties of an electron. More specifically or perhaps scientifically, the quantum numbers are used to find solutions to the Schrodinger equation. This then gives us the probability of finding an electron in a pint in space around the nucleus of an atom. Let’s learn about each quantum number in detail.

The Principal quantum number (n) gives us the size and energy of a shell. A shell is a collection of atomic orbitals which have the same principal quantum number n. an orbital is a three dimensional space around an atom where we have some probability of finding an electron. Each atomic orbital can hold 2 electrons. The Principal quantum number is represented using natural number values like 1, 2 or 3. The larger the principal quantum number, the farther is the electron from the nucleus and the larger is its energy.

The Azimuthal quantum number (l) gives us the shape of a sub-shell. The sub shell is a collection of atomic orbitals. The Principal and Azimuthal quantum numbers are related by n = l-1. For example if n=3, then l=2. The Azimuthal quantum numbers are represented by s (l=0), p (l=1), d (l=2) and f (l=3). S means that the orbital is spherical in shape, p means that the sub shell is dumble shaped, d means the subshell is double dumbled shape and f is a complex shape. See the figure below.

The number of orbitals is found using the following equation: 2l+1. For example, the p shell has 2(1)+1=3 orbitals. The number of electrons each subshell can hold is double the number of orbitals. Therefore, p has three orbitals and it can hold a total of 6 electrons.

The Magnetic quantum number (m) gives us the orientation of the orbitals in a 3D coordinate system. It also gives us the number of orbitals in a subshell.

The spin quantum number (s) gives us the spin of an electron. In case of electrons the spin has two values: +1/2 (up) and -1/2 (down).