What determines the number of elements found in each period in the periodic table?
On the basis of Quantum numbers.
Principle Quantum number is the number that tells you about the main shell in which the electron is present.And Azimuthal number is the number that tells you about the sub-shell to which the electron belongs to.
Let us consider the period 3 which consists of elements like Na,Mg,Al,Si,P,S,Cl,Ar. There are totally 8 elements by counting them. Argon's configuration is [Ne] 3s2, 3p6.
Because it is the third period the electrons can be filled only in 3s and 3p and now the orbitals present in 3s is 1 and in 3p it is 3, by adding them we get 4.
We know that each orbital contains 2 electrons and so it will be 4*2 that is it can accommodate 8 electrons.
Hence, the third period should have 8 elements.
It follows to other periods too, you can check it.
It is the filling of the electronic levels.
The first period has just two elements because the 1s level is being filled.
The second one you have 2s and 2p, therefore 8.
The third period fills 3s and 3p, therefore 8
The fourth period fills the 4s the 4p and 3d, therfore 18
The fifth period fills the 5s the 5p and 4d, therefore 18
The sixth period fills the 6s the 6p and 5d and 4f, therefore 32
The seventh period fills the 7s the 7p and 6d and 5f, therefore 32