(Original post by qiaoyu.he)
As far as I know, you only need to know the electronic configurations up to Ca, i.e. 20. Interesting things happen after element 20.
First, you need to forget the 'stable octet' rules that you were taught. It is perfectly possible for shells to have more than 8 electrons in their shells (I got very confused when I was told this in A-Level Chemistry). The maximum number of electrons that can be accommodated in any shell is 2n^2 (i.e. twice a perfect square) where n is the 'principle quantum number' (basically what shell it is). So shell 1 can accommodate 2*1^2 = 2 electrons; shell 2 can accommodate 2*2^2 = 8 electrons; shell 3 can accommodate 2*3^2 = 18 electrons; shell 4 can accommodate 2*4^2 = 32 electrons etc.
Second, each shell is also divided up into sub-shells, called atomic orbitals, which are given letters to represent them. Don't worry about the letters used, they are just names. They are called s, p, d, f, g, h, i, j and are characterized by their different shapes. Each sub-shell can accommodate exactly 2 electrons. Shell 1 has 1 s orbital; shell 2 has 1 s orbital and 3 p orbitals; shell 3 has 1 s orbital, 3 p orbitals and 5 d orbitals; shell 4 has 1 s orbital, 3p orbitals, 5 d orbitals and 7 f orbitals etc. (you get the pattern). You can see that shell 1 has 1 atomic orbital, which can accommodate 2 electrons, so shell 1 can hold 1*2 electrons in total. Shell 2 has 4 orbitals in total (1 s and 3 p), each of which can accommodate 2 electrons, so shell 2 can hold 4*2 = 8 electrons. Shell 3 has 9 orbitals in total (1 s, 3 p, and 5d), which can accommodate 9*2 = 18 electrons in total. This follows the 2n^2 rule I mentioned previously.
Shells are filled with electrons in the following order (with a few exceptions). To find any element's electronic structure, just add electrons to each orbital, down the group until that orbital is filled and then move to the next one:
Shell 1 s orbitals (2 electrons)
Shell 2 s orbitals (2 electrons)
Shell 2 p orbitals (6 electrons as there are 3 p orbitals)
Shell 3 s orbitals (2 electrons)
Shell 3 p orbitals (6 electrons)
Shell 4 s orbitals (2 electrons)
Shell 3 d orbitals (10 electrons as there are 5 d orbitals)
Shell 4 p orbitals (6 electrons)
Shell 5 s orbitals (2 electrons)
Shell 4 d orbitals (10 electrons)
There is an order to the filling, but its a bit complicated to explain. For example, carbon has 6 electrons, so it will have 2 electrons in the shell 1 s orbital, 2 electron in the shell 2 s orbital and 2 electrons in the shell 2 p orbital. Sulfur, having 16 electrons would have 2 electrons in the shell 1 s orbital, 2 electrons in the shell 2 s orbital, 6 electrons in the shell 2 p orbitals, 2 electrons in the shell 3 s orbitals and 4 electrons in the shell 3 p orbitals.
Thus you can see that Calcium, having 20 electrons will fill up to the 4 s orbital, and if you just look at shells, will have electronic structure 2,8,8,2 - exactly what you learnt. But Scandium, the first transition element has 21 electrons and the extra electron would enter the 3rd shell, in the d orbitals, giving it electronic structure 2,8,9,2.
If you continue along the periodic table, titanium will have 2,8,10,2 etc. To answer your first question, there are 10 transition metals in the 3rd period and they account for the filling of the 3rd shell d orbitals (which can accommodate 10 electrons). As they all have electrons in the 3 d shell, they all have similar properties. Interestingly, the period 4 transition metals have electrons in the shell 4 d orbitals (try to work it out and see). To answer your second question, there are no d orbitals in the second shell so there can't be transition elements in the second period.
I hope this helps (don't worry if you don't understand, I don't think transition metal chemistry should come up at GCSE). You will learn more detail about all this if you take A level chemistry. Quote me if you have any questions.