Quantum Orbital Filling for D-Block and F- Block Atoms

The nucleus of the atom is made up of protons (+) and neutrons (-); protons give us the atomic number and protons + neutrons gives us the mass number of the element

There is electrostatic repulsion between nuclei of all atoms but the electrons are responsible for the major interactions between atoms in normal chemical reactions.

The orbit or energy is not enough to portray any atom’s electron’s properties. We need to know the spatial shape and direction of the orbit (which is not always spherical, hence we say “orbital”). Each orbital has a unique set of quantum numbers, and that is what gives us the properties of each orbital.

The numbers are the quantum numbers. I just mentioned one of the 4 quantum numbers, the principal quantum energy level number” n “or shell (n = 1,2, 3 ...). Is important to note that it can be split into sub-levels (s/p/d/f), according to how many electron s you have running around.

The second number (angular quantum number “l”) defines the sub level (s/p/d/f), a sub-energy level of an electron and the spatial type of sub-shell orbital (l = 0 to n-1).For instance, an s -orbital (I=o), p- orbital (l = 1), d- orbital (l = 2), f -orbital (l = 3); for any given principal quantum number the order of energy of the sub-level is: s < p < d < f.The third number refers to the magnetic orientation of the orbital; it is “m”. For each principal quantum level n,  ( 1 s -orbital for n = 1, 2, 3;   3 p- orbitals n = 2, 3, 4;  5- d- orbitals for n =3, 4, 5;  and 7- orbitals n = 4, 5, 6 etc). So the orbital has a set of 3 numbers (n,I,m).The value of “n” gives us the size and energy of the principal orbitals (if they have the same “n” they are also called shells).For a value of “n”, the value of “I” takes integer values within (0, 1, 2, 3, .. .,) (n-l). This number gives us the shape of the orbital: s for (1=0), p for (I= I ) ,  d for (1=2), f for (1=3),  etc.

 

 

 

 

Next, for a given orbital shape, we have “m”, or the orbital’s orientation.With these 3 numbers we have the electron positioned on a specific orbital. BUT,  we still need the 4th number to identify( uniquely )any electron in an orbital, hence the spin, independent of the previous 3 numbers that belong to the orbital.

The spin is the 4th quantum number with only 2 values (+1/2/-1/2)In quantum theory, an electron can only have a very specific “quantum energy”, and to change to a different electronic level it also is required a very specific energy change.For Z=19, the 4-s orbitals are filled with electrons before the 3-d orbitals. Elements in the periodic table with partially filled 3-d orbitals are transition metals. *Z= atomic number (number of protons).

The d-block and f- block have atoms with multi electrons, and these atoms behave different: When you have atoms with many electrons, the energy of each will depend on the orbital  principal quantum number” n” and, whether the electron is in one of  s/p/d/f states.(or “I”).

WHAT HAPPENS HERE IS: the different numbers of “m”( magnetic orientation of the orbital), for that fixed set of “n” and “I”, are degenerated because  they have the same energy. Important to note that electronic configurations of these atoms are build up from ground Zero energy, and follow by occupying the lowest energy orbitals first (closer to the nucleus).

Then, because of Pauli Exclusion Principle, 2 electrons cannot have the same  set of quantum numbers and if you have 2 electrons in the same orbit they must have different spins. WHAT happens is that you can only have 2 values for the spin, an orbital with (n,1,m) can only have 2 electrons has said before.

 

 

 

 

 

 

HERE comes Hund's rule – for any given “n”, the lowest electron –energy configuration has the best possible sum of spin and  “m” values.*THIS is for the electronic configurations of atoms in the periodic table in their unexcited/ground state, if the atom is in an excited state we will have other electronic configurations.

Cu, atomic number Z=29 in the ground state: 29 electrons; possible configurations: Inner shell with 18 electrons = I    we still have 11 electrons and they will go inside the 3d and 4s orbitals; the 2 possible configurations are I3d) 4s2 and I13d’ 4s’. Both have the same spin but the second one has greater  orbital momentum; by Hund's rule the  lowest  energy configuration (ground state) is the one with greatest possible spin value  and greatest orbital momentum (I).

NOW, the orbital quantum number for the s orbital is 0 and for d is 2. Therefore, the best for Cu is the second configuration, 

Cu is an example of multi-electron atoms; these have a particular thing: the outer shell electrons have an electric field that is different from the entire  positive nuclear charge, because other electrons in inner shells hide  this  electric field  from the nucleus; therefore the outer shell electrons don’t have a full nuclear  charge  Z (atomic  number), but have like a Z (-) because it is lower than Z.