Quantum Numbers and How They Relate to the Structure of the Atom

Chemistry 11B

10/19/03

There are four quantum numbers given symbols n, l, m, and s. Every electron has a unique set these four numbers, which are used to describe its electron behavior. The first three quantum numbers give information about the size, shape, and spatial orientation of the electron cloud. The fourth quantum number describes the spin of individual electrons.

The first quantum number, n also known as the principal quantum number, is the energy level number, and gives information about the relative size of the electron cloud. It can have values 1, 2, 3, etc. The second quantum number, l is the energy sublevel number, gives information about the shape of the electron cloud. Its value can range from 0 to n – 1 or one less than the principal quantum number. If l= 0, is called an s sublevel; l= 1, is called a p sublevel, l= 2, a d sublevel, and l= 3, an f sublevel. The third quantum number, m or the orbital quantum number provides information about the orientation in space of an orbital. This quantum number can have values ranging from – l through + l. The fourth quantum number, s, called the spin quantum number represents the direction of spin of the electron, clockwise or counterclockwise. Unlike the other quantum numbers the spin number can only have one of two values +1/2 or -1/2, one representing the clockwise direction and the other counterclockwise.

The spin number is often used to distinguish between electrons in the same orbital, because if two electrons are in the same orbital the must have opposite spins. Otherwise they would have the same quantum number and according to the Pauli exclusion principal that would be impossible. The spinning of the electrons can also create magnetic fields. The four quantum numbers are each essential in determining the behavior of electrons.