
$$ \ce{num de^-=group num - oxidation state} $$
there is a general trend in atomic radii to become smaller as you travel right in the period, however it is not a nice straight line. electron repulsion effects tend to win out over an increasing effective nuclear charge. for example manganese, with a half full d shell, is quite stable and so repulsion between electrons is increased and radius increased
the increase in electron-electron repulsion is greater than the change in the effective nuclear charge and so to the right of the block atomic radii values start to rise again.
the ionisation energy depends on if the removable electrons in a paired orbital. this means that the ionisation energies are less dependant on the charge of the nucleus and more on if the electrons are already being repelled by an electron in the same orbital. the electrons will be harder to remove if they are in a singly occupied orbital and so the IE of the elements on the left are greater than those on the right
in chromium, one of the 4s electrons comes out of its orbital and jumps to a 4d orbital. this gives chromium a configuration of $\ce{4s^1, 3d^5}$. this reduces repulsion between the electrons in the 4s orbital as it goes into an unoccupied orbital
the same thing happens with copper, an electron comes out of an s orbital to form a full 3d shell and a half filled 4s shell. this means the electron configuration of copper is $\ce{4s1 3d10}$. according to aufbau the full shell experiences less repulsion than a partially filled one
the greatest oxidation state reached by the first row elements is +7 by Mn in $\ce{Mn2O7}$. this is possible due to loss of all valence electrons.
up to Mn, the greatest oxidation state for each element arises from the loss of all of their valence electrons. after this the charge on the nucleus combined with ionisation energies becomes too great and +2 states are favoured. this doesn’t mean that these ions wont form but they will be very unstable and very strong oxidsing agents


we can think of ligands and lewis bases and the metal as a lewis acid, the ligand donates a pair of electrons to form the M-L bond. using this model we can also view the metal as an electrophile and the ligand as a nucleophile

the lone pair on the ligand is donated to a vacant orbital on the metal ion