Quantum Numbers

According to quantum mechanical model or wave mechanical model of atom, orbitals represent regions in space around the nucleus where the probability of finding electrons is maximum. A large number of orbitals are possible in an atom.

To describe each electron in an atom in different orbitals, four quantum numbers are used. They are designated as n,l,m_l, and m_s.



1. Principal quantum number (n) This quantum number determines the main energy shell or level in which the electron is present. It can have whole number values starting from 1 in an atom.

The principle quantum number indicates the average distance of the electron from the nucleus. If n = 1, it is closest to the nucleus and has lowest energy.

Eariest practice was to number shells as K,L,M,N etc.
Shell with principal quantum number n = 1 is called K.
Shell with principal quantum number n = 2 is called etc.

2. Azimuthal quantum number or angular quantum number (l): This number determines the angular momentum of the electron.

It can have positive integer values from zero to (n-1) where n is the principal quantum number. For each value of n, there are n possible values of l.

For n =3, l has three values: l = 0,1,2

The earlier practice is to designate l as subshell and refer it by letters s,p,d,f,….

l=0 = s; l=1=p; l=2=d, l=3=f etc.

The energy of subshell increases with increasing value of l.

3. Magnetic quantum number ( m_l): Magnetic field acts on moving electrical charges. ( from chapters on magnetism in physics syllabus). On revolving electrons external magnetic field of the earth acts. Therefore, the electrons in a given subshell orient themselves in certain preferred regions space around the nucleus. These are called orbitals. This quantum number gives the number of orbitals for given angular quantum number l or in a given subshell.

The allowed values of m_l are –l through 0 to +l.

There are (2l+1) values of m_l for each value of l.

If l = 0, m_l has only one value. m_l = 0.

If l = 3, m_l has 7 values.
m_l = -3,-2,-1,0,1,2,3

4. Spin quantum number (m_s) : It is observed that the electron in an atom is not only revolving around the nucleus but is also spinning around its own axis. This quantum number describes the spin orientation of the electron.

The electron can spin in two ways – clockwise and anticlockwise.
Values of +1/2 and -1/2 are given to this quantum number. Its value is not dependent on other quantum numbers.

The orientations of spin are also designated by up and down arrows ↑ ↓.