It tells the main shell in which the electron resides and the approximate distance of the electron from the nucleus. This value determines to a large extent energy of the orbital. It also tells the maximum number of electrons a shell can accommodate is `2n^2`, where n is the principal quantum number.

`tt((text(Shell), K,L, M,N),(text(Principle quantum number n), 1,2,3,4),(text(Maximum number of electrons), 2,8,18,32))`

Permissible values of n: all positive integers.

This represents the number of subshells present in the main shell. These subsidiary orbits within a shell will be denoted as `s,p,d,f` ... This tells the shape of the sub shells. The orbital angular momentum of the electron is given as:

`sqrt (l(l+1)) h//2pi` or `sqrt (l(l+1)) h` for a particular value of `l` where `h = h//2 pi`

For a given value of `n`, possible values of `s` vary from `0` to `n - 1`. This means that there are `n` possible shapes in the `n^(th)` shell.

An electron due to its angular motion around the nucleus generates an electric field. This electric field is expected to produce a magnetic field. Under the influence of external magnetic field, the electrons of a subshell can orient themselves in certain preferred regions of space around the nucleus called orbitals. The magnetic quantum number determines the number of preferred orientations of the electron present in a subshell. The values allowed depends on the value of `l` , the angular momentum quantum number, `m` can, assume all integral values between `- t` to `+ t` including zero. Thus `m` can be `-1 , 0, + 1` for , `l = 1`. Total values of `m` associated with a particular value of `l` are given by `2 l + 1`

Just like earth not only revolves around the sun but also spins about its own axis, an electron in an atom not only revolves around the nucleus but also spins about its own axis. Since an electron can spin either in clockwise direction or in anticlockwise direction, therefore, for any particular value of magnetic quantum number, spin quantum number can have two values, i.e., `+ 1/2` and `- 1/2` or these are represented by two arrows pointing in the opposite directions, i.e., and `-` . When an electron goes to a vacant orbital, it can have a clockwise or anticlockwise spin. This quantum number helps to explain the magnetic properties of the substances.

Spin angular momentum `mu_s = sqrt (s(s+1)) xx h/(2pi)` where `s= 1/2`

Another term, defined as multiplicity is given as `2 |S|+ 1 ` where `|S|` is total spin

= no. of unpaired electrons `xx 1/2`.

Can you derive the following expressions?

1. no. of orbital `= n^2` or ` (2l +1)` for `'n'` `l` respectively

2. no. of `e^(-) = 2n^2` or `2(2l+1)` for `'n'` `l` respectively

Nodes : The region where the probability of finding an electron is zero or the probability density function reduces to zero is called a nodal surface or simply nodes. Nodes are classified as radial nodes and angular nodes .
In general, an orbital with principal quantum number `= n` and azimuthal quantum number `= I`, has

Total nodes `= n - 7` ; Radial nodes `= n - l -1`;

Angular nodes `= l` ; At Nodes, `y^2 =0, y=0`