The behavior of *electrons* in space around the nucleus is described by a set of four numbers called quantum numbers.

Schrodinger equation has been solved for hydrogen atom. There are many solutions to this equation. Quantum re sets of numerical values, which give acceptable solutions to Schrödinger equation for hydrogen atom.

Three quantum numbers are obtained by solving Schrödinger wave equation while spin quantum number is due to the two different orientations of electron in a magnetic field. i.e. clockwise & anticlockwise.

Four quantum numbers are

## PRINCIPAL QUANTUM NUMBER (n)

• It gives information about shells.

• It shows the approximate distance of electron from the nucleus of an atom.

• It was called orbit by Bohr. It is called orbit by Bohr. It is called principle quantum number by Schrodinger.

• Its values are: n = 1, 2, 3 … It cannot have zero value.

• Value of ‘ n ‘ tells about the energy and distance of electron from the nucleus.

Greater the value of n, greater will be the energy and distance of electron from the nucleus & vice versa.

It is the measure of size of electronic shell.

• The value of n corresponds to a definite shell e.g.

• The electrons in a shell can be determined by the formula 2n²

## AZIMUTHAL QUANTUM NUMBER

It gives information about subshells.

### Origin of Azimuthal Quantum Number

A spectrometer of high resolving power shows that an individual line in a line spectrum of an atom is actually further divided into several fine lines. This is called fine structure. It means than an individual shell is further divided into several sub-shells. These sub-shells are explained in terms of azimuthal quantum number. The azimuthal quantum number is denoted by “l” Its values depend upon the value of ‘n’.

It has value from 0, 1, 2, 3…(n-1).

● The numbers 0, 1, 2, 3 … corresponds for various subshells.

O stands for s – subshell means ‘ sharp 1 stands for p – subshell means ‘principle’

2 stands for d – subshell means ‘diffused’ 3 stands for f – subshell means ‘fundamentals’

These terms are used to describe the series of lines in the spectrum.

### Number of Electrons in a Sub-Shell

● It describes the shape of a subshell in which the electron is present. A maximum number of electrons in a subshell can be obtained by using the formula 2 (2L + 1). Thus

### Shape of Sub-Shells

Value of “L” also tells us about the shape of orbital.

A brief summary is given below.

### Relationship between Principal and Azimuthal Quantum No

The relationship is as follows

## MAGNETIC QUANTUM NUMBER (m)

It gives information about the different orientations of orbitals in space.

### Origin of Magnetic Quantum Number

● In the presence of a magnetic field, lines in the line spectrum of an atom are further spilled up into various very fine lines. The appearance of these lines is explained by magnetic quantum numbers.

● It is represented by ‘m’.

● It gives the orientation and degeneracy of the orbital in space. Hence, it is also called the orbital orientation quantum number.

● It has a value depends upon the value of ‘L’. Thus, m = -L … 0 .. + L or m = 0. = +-L.

● The value of ‘m’ shows the different ways in which a particular orbital can be arranged in space.

● It shows that s – orbital can be arranged in space only in one way. Thus, it is not further subdivided into other orbitals. It is a spherical and symmetrical orbital. In this probability of finding an electron is the same in all directions.

● It means that p-orbital have three possible orientations in space. Thus, p – orbital is further sub- divided into three orbitals along X, Y and Z- axis called orbital axis. These three orbitals are present perpendicular to each other.

● In the absence of magnetic field all the three p – orbitals have same energy. These are called 3 – fold degenerate or triply degenerate orbitals.

● Formula for number of possible orientation of orbitals.

● For a given value of t, the total values of ‘m’ are (2L + 1).

Thus for

## SPIN QUANTUM NUMBER (s)

It describes the spin of electron is an atom. It is denoted by ‘s’.

### Origin of Spin Quantum Number

● Alkali metals have one electron in their valence shell. When this electron jumps from the excited state to the ground state, it emits light and forms a line spectrum. A high resolving spectrometer shows that each line in the line emission spectrum consists of two lines. This is called doublet structure. This doublet structure is different from the fine line structure, which is explained by the azimuthal quantum number.

● The lines explained by azimuthal quantum number are closely spaced, while in doublet structure two lines are widely spaced.

● In 1925, Goudsmit and Uhlenbeck suggested, that an electron also revolve about its axis . This is called self – rotation. It may be clockwise or anticlockwise. So an electron generates two opposite magnetic fields due to two opposite spins. This spin motion produces doublet line structure in the emission spectrum of an atom. It can be explained by spin quantum number.

● The spin quantum number of an electron may be +1/2 or -1/2

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