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Azimuthal Quantum Number


An atom consists of different types of orbits. These orbitals are formed according to the quantum numbers. Three important types of quantum numbers named principal, azimuthal and magnetic quantum numbers are responsible for the shape, orientation and energy of orbitals. In order to describe an electron, another quantum number is required, which is termed as spin quantum number. This will helps to explain the spin of an electron.


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Sommerfield proposed the azimuthal quantum number. Angular momentum of an electron can determined by this quantum number using the given formula,
Angular momentum = $\sqrt{l(l+1)}$$\times$$\frac{h}{2\pi}$
The values of the azimuthal quantum number ranges 0 to (n-1), where n is the principal quantum number.

How to Find Azimuthal Quantum Number?

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Azimuthal quantum number l may have all possible whole number values from 0 to (n-1) i.e., l = 0, 1, 2, ....., (n-1). So the l value can be calculated according to the value of n. If n = 1, the l value become 0. l value is 0 to (n-1) value of a particular n value. By using this formula we can calculate the l value of any n value.


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This quantum number accounts for the appearance of a group of closely spaced lines in hydrogen spectrum. The energy associated with angular momentum of an electron must be well within its total energy determined by n. Thus, electrons in an atom are grouped not only in main energy levels given by, n but also into energy sub levels given by l. The value of l gives sub shells in which electron is located. The number of sub shells within a principal shell is determined by value of n for that principal energy levels. If n = 2; the l value = 0,n = 3; l = 0,1,2

l Value
Corresponding Sub shell
0 s
1 p
2 d
3 f
4 g