What are the relatioships between group configuration and group number for elements in the s, p and d blocks?
It is because of their atomic properties: atomic radius, first ionization energies, electron affinity and electronegativity.
Ohhh boy. I did a quick google search and I learned that the s, p, and d blocks are essentially metals, transition metals, and non-metals, with some exceptions.
There are 4 factors that affect why elements are placed where they are; atomic radius, first ionization energies, electron affinity and electronegativity. The last two are quite similar to the second one so I won't talk about it.
S-BLOCK: As the atomic radius increases in a group, the atomic radius also increases, specifically the Alkali family. This is because every period on the PT represents a new valence shell. Alkali metals have only one valence electron and are thus extremely reactive. Their reactivity indicates that their first ionization energies are very low, meaning the attraction levels with the atom are very weak, indicating a larger radius between the nucleus and the electron shells. As we go down the the family, more shells are added. Thus, their atomic radius increases.
P-BLOCK: Coincidentally, as the atomic number increases in a period, the atomic radius decreases. This is due to their valence electrons and attraction within the atom. The Noble Gases family specifically, are the most stable elements on the PT (octet elements). Having a full composition of electrons shows unreactivity. That said, the attraction within the atom is very strong. So strong that its atomic radius decreases.
In summary, the elements are placed on the PT based on their atomic properties. I only outlined two of them, the other two are similar to first ionization energy.
Hope this helps and you didn't cry at the information :)