Azimuthal or Angular Quantum Number (l)

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This quantum number denotes the sub-level or subshell in a given principal energy shell to which an electron belongs. This is also called secondary quantum number. It is denoted by l and corresponding to each value of n, there are n possible values of l ranging from zero to one less than n for that state i.e., l = 0, 1, 2...(n - 1).

This quantum number gives the energy of an electron due to the angular momentum of the electron. The relation between angular momentum of the electron and l is

Each value of l represents a particular sub-shell or sub-level. For e.g., for n = 3, l can have three values, that is, l = 0,1,2.

This means that there are three sub-levels in the third energy level. The various sub-levels or sub-shells are also designated by letters s, p, d, f depending upon the values of l as shown below:

* These symbols arise from the spectroscopic terms: s(sharp), p(principal), d(diffuse), f(fundamental). After f the designations follow alphabetical order i.e., l = 4 is designated as g.

Thus, for n = 1, l = 0.

This means that first principal energy level consists of only one sub-level termed as s or specifically 1s; where the number before the level represents principal energy level.

Similarly, for n = 2, l = 0, 1.

This means second principal energy level consists of two sub-levels 2s and 2p.

For n = 3, l = 0, 1, 2. .

This means third principal energy level consists of three sub-levels 3s, 3p and 3d.

For n = 4, l = 0, 1, 2, 3.

This means fourth principal energy level consists of four sub-levels 4s, 4p, 4d and 4f.

From this, it may be concluded that the number of sub-levels in a principal energy level is equal to the value of n. Thus, there is only one sub-level in first energy level (n=1), two in second (n=2), three in third energy level (n=3) and so on.

Thus, angular quantum number determines the sub-level in a given principal energy level. In a given energy level, the order of energy of different sublevels is (except for hydrogen) s < p < d < f.