Pauli’s Exclusion Principle
After studying the electronic configuration it is not time to take a look at a very important concept known as Pauli’s exclusion principle and stated in simple terms, it states that within an atom, all electrons have unique set of quantum numbers. This means to say that all the four quantum numbers of an atom cannot match in totality with any other electron within the same atom. Of course there can be a maximum match of 3 quantum numbers at the most, but never all four will be the same.
Infact the total number of electrons is a particular shell (as discussed in above section also) can be deduced from this principle and that is why the maximum number of electrons in the shells have their upper limit fixed. Say for example the K shell cannot have more than 2 electrons, while N shell can have max of 32 electrons and so forth. This principle has been verified by experimental results as well. Let us see an simple actual deduction pertaining to the L shell as follows.
We know that for the L shell n = 2.
So the corresponding values of l are 0 and 1
For l = 0 sub-shell, we have only one sub-shell and hence one orbital magnetic quantum number and two spin quantum numbers. This means that if there are more than two electrons the Pauli’s principle will be violated, hence the maximum number of electrons in first sub-shell of L is 2. Similarly it can be reasoned that the maximum number of electrons in second sub-shell is 6.
This means that the total number of electrons in L shell is 8. For your convenience I have given the detailed breakdown of various shells, sub-shells and electron numbers in a tabular format below so that you can check at a single glance.
After having studied the basics of quantum numbers and energy bands, we will now proceed to study about types of bands which would ultimately lead us to the study of semiconductors which form the basis of digital electronics.