Quantum Theory and the Electronic Structure of Atoms Part 2 Unit 4, Presentation 1

QUANTUM NUMBERS The shape, size, and energy of each orbital is a function of 3 quantum numbers which describe the location of an electron within an atom or ion n (principal) ---> energy level l (orbital) ---> shape of orbital m l (magnetic) ---> designates a particular suborbital The fourth quantum number is not derived from the wave function s(spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½) s (spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½)

Schrodinger Wave Equation  fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1 n=2 n=3 distance of e - from the nucleus

e - density (1s orbital) falls off rapidly as distance from nucleus increases Where 90% of the e - density is found for the 1s orbital

Types of Orbitals ( l ) s orbital p orbital d orbital

l = 0 (s orbitals) l = 1 (p orbitals)

p Orbitals this is a p sublevel with 3 orbitals These are called x, y, and z this is a p sublevel with 3 orbitals These are called x, y, and z 3p y orbital

p Orbitals The three p orbitals lie 90 o apart in spaceThe three p orbitals lie 90 o apart in space

l = 2 (d orbitals)

f Orbitals For l = 3, f sublevel with 7 orbitals

 = fn(n, l, m l, m s ) magnetic quantum number m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation

m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2

 = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½

Energy of orbitals in a single electron atom Energy only depends on principal quantum number n n=1 n=2 n=3

Energy of orbitals in a multi-electron atom Energy depends on n and l

“Fill up” electrons in lowest energy orbitals (Aufbau principle)

The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).

Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

Why are d and f orbitals always in lower energy levels? d and f orbitals require LARGE amounts of energy It’s better (lower in energy) to skip a sublevel that requires a large amount of energy (d and f orbtials) for one in a higher level but lower energy This is the reason for the diagonal rule! BE SURE TO FOLLOW THE ARROWS IN ORDER!

Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. 1s 1 principal quantum number n angular momentum quantum number l number of electrons in the orbital or subshell Orbital diagram H 1s 1

What is the electron configuration of Mg? Mg What are the possible quantum numbers for the last (outermost) electron in Cl? Cl

Outermost subshell being filled with electrons

Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

Exceptions to the Aufbau Principle Remember d and f orbitals require LARGE amounts of energy If we can’t fill these sublevels, then the next best thing is to be HALF full (one electron in each orbital in the sublevel) There are many exceptions, but the most common ones are d 4 and d 9 For the purposes of this class, we are going to assume that ALL atoms (or ions) that end in d 4 or d 9 are exceptions to the rule. This may or may not be true, it just depends on the atom.

Exceptions to the Aufbau Principle d 4 is one electron short of being HALF full In order to become more stable (require less energy), one of the closest s electrons will actually go into the d, making it d 5 instead of d 4. For example: Cr would be [Ar] 4s 2 3d 4, but since this ends exactly with a d 4 it is an exception to the rule. Thus, Cr should be [Ar] 4s 1 3d 5. Procedure: Find the closest s orbital. Steal one electron from it, and add it to the d.

Try These! Write the shorthand notation for: Cu Ag Cu

Keep an Eye On Those Ions! Electrons are lost or gained like they always are with ions… negative ions have gained electrons, positive ions have lost electrons The electrons that are lost or gained should be added/removed from the highest energy level (not the highest orbital in energy!)

Keep an Eye On Those Ions! Tin Atom: Sn +2 ion: Sn +4 ion: Note that the electrons typically came out of the highest energy level, not the highest energy orbital!