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# Quantum Numbers

Quantum numbers are numbers assigned to all the electrons in an atom and they describe certain characteristics of the electron. It is very important to understand Quantum Numbers in order to understand the Structure of Atom. In this chapter, we’ll learn everything about Quantum Numbers.

### Suggested Videos        Shape of s Orbital Development leading to Bohr's model of atom Introduction to Quantum Numbers  ## Quantum Number

An atom consists of a large number of orbitals which are distinguished from each other on the basis of their shape, size and orientation in space. The orbital characteristics are used to define the state of an electron completely and are expressed in terms of three numbers as stated, Principal quantum number, Azimuthal quantum number and Magnetic quantum number and Spin Quantum number. Quantum number are those numbers that designate and distinguish various atomic orbitals and electrons present in an atom. A set of four numbers through which we can get the complete information about all the electrons in an atom, be it energy, location, space, type of orbital occupied, and even the orientation of that orbital is called Quantum Numbers.

### Principal Quantum Number

The Principal Quantum Number represents the principal energy level or shell in which an electron revolves around the nucleus. It is denoted by the letter n and can have any integral value except the 0 i.e. n = 1, 2, 3, 4 … ….etc. The energies of the various principal shells will follow the sequence as :

K < L < M < N < O…..

1 < 2 < 3 < 4 < 5…….

### Azimuthal Quantum Number

Azimuthal quantum number, also known as orbital quantum number determines the subshell to which an electron belongs. As a matter of result, the number of electronic jump increases and the number of lines at the same time.

• For a given value of n, it can have any integral value ranging from 0 to n – 1.
• For the 1st Shell, say K, n =1,  you can have only one value i.e. l = 0
• For the 2nd Shell, say L, n = 2, you can have two values  i.e. l = 0 and 1
• For the 3rd Shell, say M, n = 3, you can have three values i.e. l = 0, 1 and 2
• For the 4th shells, say N, n = 4, you can have 4 values i.e. l = 0, 1, 2 and 3  ### Magnetic Quantum Number

Magnetic Quantum Number denoted by the symbol m is what represents the orientation of atomic orbital in space. The value of the Magnetic Quantum Number, m, depends on the value of l. Magnetic Quantum Number can have a total number of (2l + 1).

 Sublevel l ml s 0 0 p 1 -1, 0, +1 d 2 -2, -1, 0, +1, +2 f 3 -3, -2, -1, 0, +1, +2, +3

### Spin Quantum Number

Spin Quantum Number represents the direction of the spin of the electrons. This can either be in the direction of clockwise or even anti-clockwise. Spin Quantum Number is denoted by the symbol s. It can have about only two values i.e. +1/2 or -1/2

## Solved Examples for You

Question: An electron is in one of the 3d orbitals. Give the possible values of n, l and ml for this electron.

Solution: For the 3d orbital,

• Principal quantum number (n) = 3
• Azimuthal quantum number (l) = 2
• Magnetic quantum number (ml) = – 2 , – 1 , 0 , 1, 2

Question: Calculate the minimum and maximum number of electrons which have magnetic quantum number m= 1 and spin quantum number s= 1/2 in chromium

Solution: Spin can either be +1/2 or -1/2. So it is 2 electrons. If one has spin +1/2, other will have spin -1/2. So it is 2 electrons.

Question: Give the physical significance of Principal Quantum Number.

Solution: The principal quantum number (n)  signifies the size of the electron cloud.

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