Electronic configuration & quantum numbers

Electronic configuration: The distribution of electrons in an atom is known as electronic configuration. Spectroscopic studies, which are used in elucidating electronic configuration show that four numbers known as quantum numbers are required to characterize each electron in an atom.

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Principal Quantum number (n)

Principal Quantum number (n): It represents the main electronic energy shells from the nucleus. It can take only integer values like 1, 2, 3, 4 ….etc. The corresponding shells are also known as K, L, M, N shells respectively.

In the absence of an external field, it mainly decides the energy of the electron in the orbit. It also gives the number of electrons that may be accommodated in each shell, the capacity of each shell being given as 2n². The principal quantum number decides the size of a shell.

Azimuthal Quantum number (l):

Azimuthal Quantum number (l): It represents the sub­shells in an orbit.
The sub­shells (l) in any shell(n) can have the values 0 to (n – 1). It gives the shape of the shell.

When l = 0, the sub­shell is called s sub­shell. Similarly when l = 1, 2, and 3 the subshells are called p,d, and f sub­shells respectively.

When n = 1, l can have only one value i.e. zero. Hence in 1st orbit, there is one sub­orbit which may be represented as 1s.

When n = 2, l can have 2 values namely 0 and 1, which means that the second shell has two sub­shell represented as 2s and 2p respectively.

Likewise, when n = 3, we have three sub­shells designated as 3s, 3p, and 3d with corresponding l values 0, 1, and 2.

The 4th shell (n = 4) has four subshells (4s, 4p, 4d, and 4f ) with l values 0, 1, 2, and 3.

The total number of sub­shells in any shell is the same as the principal quantum number(n).

Magnetic Quantum Number (m)

Magnetic Quantum Number (m): This gives the number of orbitals in a sub­shell. It takes only integer values from –l to + l through zero.
m = 2l + 1 for any value of l. E.g., when l = 0, m = 1. m decides the orientation of electrons.

Hence, in s sub­shell there is only one orbital. [Since, l=0, m=(2l+1) =2.0 +1 = 1].
In p subshell, there are 3 orbitals. [Since, l=1, m=(2l+1) = 2.1 + 1 =3].

The 3 orbitals are designated as p_x, p_y, and p_z where x, y, and z refer to the axes perpendicular to each other in space.

In d subshell there are 5 orbitals [Since, l=2, m=(2l+1) = 2.2 + 1 =5]
In f subshell there are 7 orbitals [Since, l=3, m=(2l+1) = 2.3 + 1 =7]

Spin Quantum number (s)

Spin Quantum number (s): When an electron rotates around a nucleus, it also spins about its own axis. If the spin is clockwise, its spin quantum number is +1/2 and it is represented by an upward arrow­. If the spin is anticlockwise, its value is –1/2 and it is represented by a downward arrow­.

If s (Spin Quantum number ) value is +1/2, then by convention, we take that electron as the first electron in that orbitals and when s(Spin Quantum number) value is –1/2, it is taken as the second electron.