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Write short notes on Quantum number and orbitals.

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Quantum number and orbitals: 

Quantum numbers are a set of four numbers with the help of which we can get complete information about all the electrons in an atom, i.e. location, energy, the type of orbital occupied, shape and orientation of that orbital. 

There are 4 quantum numbers:

Principle quantum Azimuthal quantum number Magnetic quantum number Spin quantum number
It was proposed by Bohr and denoted by 'n' It was proposed by sommerfild and is denoted by 'l'. Also known as angular quantum number It was proposed by Zeeman and is denoted by 'm' It was given by Goldschmidt and Uhlenbeck and denoted by symbol 's'
It determine the main energy shell or level in which electron is present It determine the number of sub-shells or sublevels to which the electrons present It gives number of permitted orientations or orbitals of sub-shells The value of 's' is +1/2 and -1/2 which signifies the spin or rotation or direction of electron on its own axis.
It determine the average distance between electron and nucleus i.e., it denotes size of atom. It tells about the shape of orbitals. It tells about spliting of spectral lines in magnetic field i.e., Zeeman Effect. The spin may be clockwise or anti clockwise.
The maximum number of electron in an orbit represented by this quantum number is 2n2 The value of l = (n - 1), where 'n' denotes principle quantum number. For a given value of 'n' a total value of 'l' is equal to value of 'n' The value of 'm' varies from 'l' through zero to +1. For a given value of 'l' total value of 'm' is equal to (2l + 1). maximum spin of an atom = \(\frac{1}{2}\) x number of unpaired electron
All the orbitals of given value of n constitute a single shell of atom and represented as The maximum number of electron in sub-shell is 2(2l + 1) For a given value of 'n' total value of 'm' is equal to n2
Designation
Shape Subshell orbital
n      shell 0 s(sharp spherical) a         1
1      K 1 p(principle) Dumbbell p         3
2      L 2 d(diffused Double dumb-bell) d         5
3      M f          7
4      N 3 f(fundamental complex) Ex: if n = 2, l = (2 - 1) = 1
i.e., 'p'
\(\therefore\) m = 3 i.e., -1, 0, +1

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