Chapter 7 - Multi-Electron Species and Periodic Properties

01/11/26

that fuckass diagram at the start of the chapter

nodes only exist for the orbital they pertain to.

a 1s radial probability distribution is going to have overlap with spaces included in the 2s orbital. the node for the 2s orbital exists within the space the 1s also exists in

this means nothing to the 1s orbital. it dgaf abt the 2s’s node.

as well, this introduced the idea of electron penetration, where the ability of the 2s orbital to have the electron right close to the nucleus (essentially within the same space as the 1s) can change the Z_eff felt by that electron, as opposed to what it would feel if it were in the outer portion of the 2s. (prolly not important yet)

what does this thing mean?

its a graphical representation of the energy associated with each of the subshells for each quantum state. but it shows that they are no longer degenerate anymore (when referring to multi-electron atoms)

effective nuclear charge

this is the nuclear charge that a valence electron actually feels.

an approximation for it is Z-S, where Z is the amount of protons in the nucleus and S is the number of shielding, (non-valence) electrons

trends in effective nuclear charge

• Z_eff increases as you go L to R in a period, as Z increases, but S remains the same

• note, electrons are only shielded by more inner electrons, not the ones behind or beside them. often, this is the two electrons

the spin quantum number

an electron can have two different magnetic moments, meaning the electron can interact with a magnetic field in two possible ways, which we use a fourth quantum number m_s to describe, with two allowed values:+- ½

a positive m_s represents “spin up“, and a negative represents “spin down“. spin up can be show as a half-headed arrow pointing up, and vice versa, in something known as an orbital diagram

electron configuration

chemists write electron configurations to communicate how the electrons in a multi-electron atom or ion are distributed amongst the atomic orbitals. they can be condensed or non condensed

ex: 1s²2s¹

or ex: [Ar] 4s²3d⁶, which uses [Ar] to represent all of the electron configuration of periods 1, 2, and 3, and then we actually write out where we see variance, in the fourth period

electron filling rules

• aufbau principle

• pauli exclusion principle

• hund’s rule

aufbau principle

• the “building up“ principle

• mandates filling orbital with electrons from the lowest energy first

pauli exclusion principle

• states no two electrons in an atom or ion may have the same four quantum numbers (i.e. you can’t have two spin up in one orbital)

• this one can never be violated

what is hund’s rule

• states that when orbitals with the same energy (degenerate are available, electrons occupy them singly with the same spin before being paired within an orbital

• i.e. if you’re filling the 3p orbitals, you will have to fill them all with an up spin electron before starting into pairing them with down spin ones in each orbital

procedure for writing electron configurations

1. locate the element in the periodic table, noting the period that the element is in (which is the n value) and the block (s, p, d, f)

2. identify the noble gas in the previous period (n-1) and write its symbol in square brackets ex: [Ar]

3. startsing from the left hand side of the periodic table in period n, write the subshells and occupancies in order until the element is reached

4. for ionic species (of the s or p blocks) simply add or subtract the amount of electrons it has for a charge

orbital filling order graphic

the order is:

1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p⁶, 6s², 4f¹⁴, 5d¹⁰, 6p⁶, 7s²

there are two exceptions to orbital filling

1. copper and chromium

2. transition metal (d block ions)

the copper and chromium exception

these two atoms prefer spin symmetry, i.e. all of their arrows must go in one direction, and they will move electrons from one orbital into another to do it.

transitional metal (d block) ions

when transition metals are ionized, it is experimentally observed that the remaining electrons will be found in the d subshell of the valence shell.

i.e., if its an ionized trans. metal, , they will move electrons out of the s shell to put them in the d shell

ex: manganese (II) ion is [Ar]3d⁵

ground and excited states for multi-electron species

the ground state for any orbital diagram will NOT violate any of the rules

an excited state will violate the rules, (except for the Pauli exclusion principle).

there are inf many excited state diagrams, but only one correct ground state diagram for each atom.

magnetism

species can be paramagnetic or diamagnetic

paramagnetic

species with one or more unpaired electrons (i.e. their orbital diagram doesn’t have filled ups and downs)

diamagnetic

species with no unpaired electrons (i.e.e all are spin paired) are called diamagnetic