Which Are Allowable Sets of Quantum Numbers?

Quantum numbers are used to describe the energy and shape of an electron orbital within an atom. These numbers are represented by the letters n, l, m and s. The energy level quantum number, represented by the letter n, represents the energy of the electron within the orbital. This number can be equal to (1,2,3,4...). The higher the number, the further away the orbital is from the nucleus.

The angular quantum number, represented by l, indicates the direction of the orbit. It describes the shape of the electron orbit. The integers allowable for l range from 0 to (n-1). The third number, the magnetic quantum number, relates to the direction of the electrons' orbit. "m" has an allowable set of integers that range from -l to +l. The fourth and final quantum number, represented by s, is called the spin quantum number. Only two integers are allowable for this number: +1/2 indicating a 'spin up' electron and -1/2 indicating a 'spin down' electron.

Scientists initially believed that electrons traveled around the nucleus in a similar fashion to how the planets orbit around the sun. With only one quantum number (n) to represent the orbit, the Bohr model was incomplete. Later, the Schr?dinger equation compared the movements of electrons around the nucleus to a cloud, introducing the other three quantum numbers.