Quantum Theory Schrodinger Heisenberg http://www.colby.edu/chemistry/CH141F/Chapter%206%20presentation.ppt Quantum Theory Schrodinger Heisenberg http://staff.science.nus.edu.sg/~PC1144/PC1144%20Lectures/lecture16.ppt

The Quantum Mechanical Model Energy is quantized. It comes in chunks. A quanta is the amount of energy needed to move from one energy level to another. Since the energy of an atom is never “in between” there must be a quantum leap in energy. Schrodinger derived an equation that described the energy and position of the electrons in an atom

The Quantum Mechanical Model Heisenberg Uncertainty Principle---it is impossible to know both the exact position and momentum of an object at the same time. Can’t know position if e- is moving. Can’t know momentum if e- is not moving.

The Quantum Mechanical Model Has energy levels for electrons. Orbits are not circular. It can only tell us the probability of finding an electron a certain distance from the nucleus.

The Quantum Mechanical Model The atom is found inside a blurry “electron cloud” A area where there is a chance of finding an electron. Draw a line at 90 %

Schrodinger’s Quantum #’s (n) Principal quantum # n = 1, 2, 3 … -1 the energy level of the electron. Formula: 2(n)2 = # of electrons per energy level (l) Azimuthal or Secondary quantum # l = 0,1, 2, (n-1) the sublevels or shape within an energy level. s,p,d,f (names of sublevels) s,p,d, & f each have a unique shape.

Quantum #’s (cont.) (ml) magnetic quantum # (ms) spin quantum # ml = +l .. 0 .. –l (2l +1) = total orbitals regions where there is a high probability of finding an electron each orbital can hold 2 e- (ms) spin quantum # ms = +1/2 or –1/2 in each orbital there can be up to 2 electrons spinning in opposite directions. Clockwise  +1/2 Counter clockwise  –1/2

Quantum Numbers n Principle Azimuthal m l Magnetic ms Spin l l = 0, 1, 2, 3 … (n-1) m l Magnetic m l = +l ..+2,+l, 0,. –l, -2.. -l ms Spin ms = +1/2 or –1/2 s p d f

Arrangement of Electrons in Atoms Electrons in atoms are arranged as LEVELS (n) SUBLEVELS (l) ORBITALS (ml)

Energy Levels Each energy level has a number called the PRINCIPAL QUANTUM NUMBER, n Currently n can be 1 thru 7, because there are 7 periods on the periodic table

Energy Levels n = 1 n = 2 n = 3 n = 4

Orbitals and the Periodic Table Orbitals grouped in s, p, d, and f orbitals (sharp, proximal, diffuse, and fundamental) s orbitals d orbitals p orbitals f orbitals

s orbitals 3s 2s 1s 1 s orbital for every energy level Spherical shaped Each s orbital can hold 2 electrons Called the 1s, 2s, 3s, etc.. orbitals. 3s 2s 1s

p orbitals Start at the second energy level 3 different directions 3 different shapes Each can hold 2 electrons

d orbitals Start at the third energy level 5 different shapes Each can hold 2 electrons

f orbitals Start at the fourth energy level Have seven different shapes 2 electrons per shape

f orbitals

Summary # of orbitals Max electrons Starts at energy level s 1 2 1 p 3 6 2 d 5 10 3 7 14 4 f

Number of Electrons that can be held in each orbital s = 2 e- p = 6 e- d = 10 e- f = 14 e-

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p

Electron Configurations The way electrons are arranged in atoms. Aufbau principle- electrons enter the lowest energy first. This causes difficulties because of the overlap of orbitals of different energies. Pauli Exclusion Principle- at most 2 electrons per orbital - different spins Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to .

Electron Configuration Let’s determine the electron configuration for Phosphorus (P) Need to account for 15 electrons

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p The first to electrons go into the 1s orbital Notice the opposite spins only 13 more

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p The next electrons go into the 2s orbital only 11 more

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p The next electrons go into the 2p orbital only 5 more

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p The next electrons go into the 3s orbital only 3 more

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s The last three electrons go into the 3p orbitals. They each go into seperate shapes 3 upaired electrons 1s22s22p63s23p3

The easy way to remember 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2 electrons

Fill from the bottom up following the arrows 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 4 electrons

Fill from the bottom up following the arrows 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 12 electrons

Fill from the bottom up following the arrows 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 20 electrons

Fill from the bottom up following the arrows 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 38 electrons

Fill from the bottom up following the arrows 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 56 electrons

Fill from the bottom up following the arrows 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 88 electrons

Fill from the bottom up following the arrows 7s 7p 7d 7f 6s 6p 6d 6f 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s 108 electrons

Effective Nuclear Charge Electrostatic repulsion between negatively charged electrons Influences the energies of the orbitals. The effect of repulsion is described as screening or shielding. The combined effect of attraction to the nucleus and repulsion from other electrons gives an effective nuclear charge, Zeff, which is less than that of the ‘bare’ nucleus. Zeff = Z - S + # Protons # Shielding electrons

Periodicity of Effective Nuclear Charge Z* on valence electrons

Effective Nuclear Charge, Zeff Atom Zeff Experienced by Electrons in Valence Orbitals Li +1 Be +2 B +3 C +4 N +5 O +6 F +7 Increase in Zeff across a period

Electron Configurations A list of all the electrons in an atom (or ion) Must go in order (Aufbau principle) 2 electrons per orbital, maximum We need electron configurations so that we can determine the number of electrons in the outermost energy level. These are called valence electrons. The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14… etc.

Electron Configurations 2p4 Number of electrons in the sublevel Energy Level Sublevel 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14… etc.

Let’s Try It! Write the electron configuration for the following elements: H Li N Ne K Zn Pb

Shorthand Notation A way of abbreviating long electron configurations Since we are only concerned about the outermost electrons, we can skip to places we know are completely full (noble gases), and then finish the configuration

Shorthand Notation Step 1: Find the closest noble gas to the atom (or ion), WITHOUT GOING OVER the number of electrons in the atom (or ion). Write the noble gas in brackets [ ]. Step 2: Find where to resume by finding the next energy level. Step 3: Resume the configuration until it’s finished.

Shorthand Notation [Ne] 3s2 3p5 Chlorine Longhand is 1s2 2s2 2p6 3s2 3p5 You can abbreviate the first 10 electrons with a noble gas, Neon. [Ne] replaces 1s2 2s2 2p6 The next energy level after Neon is 3 So you start at level 3 on the diagonal rule (all levels start with s) and finish the configuration by adding 7 more electrons to bring the total to 17 [Ne] 3s2 3p5

Practice Shorthand Notation Write the shorthand notation for each of the following atoms: Cl K Ca I Bi

Valence Electrons Electrons are divided between core and valence electrons B 1s2 2s2 2p1 Core = [He] , valence = 2s2 2p1 Br [Ar] 3d10 4s2 4p5 Core = [Ar] 3d10 , valence = 4s2 4p5

Rules of the Game No. of valence electrons of a main group atom = Group number (for A groups) Atoms like to either empty or fill their outermost level. Since the outer level contains two s electrons and six p electrons (d & f are always in lower levels), the optimum number of electrons is eight. This is called the octet rule.

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: [Kr] 5s2 4d10 5p2 Sn+4 ion: [Kr] 4d10 Sn+2 ion: [Kr] 5s2 4d10 Note that the electrons came out of the highest energy level, not the highest energy orbital!

Keep an Eye On Those Ions! Bromine Atom: [Ar] 4s2 3d10 4p5 Br- ion: [Ar] 4s2 3d10 4p6 Note that the electrons went into the highest energy level, not the highest energy orbital!

Try Some Ions! Write the longhand notation for these: F- Li+ Mg+2 Write the shorthand notation for these: Br- Ba+2 Al+3

Exceptions to Electron Configuration

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 d4 and d9 For the purposes of this class, we are going to assume that ALL atoms (or ions) that end in d4 or d9 are exceptions to the rule. This may or may not be true, it just depends on the atom.

Exceptions to the Aufbau Principle d4 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 d5 instead of d4. For example: Cr would be [Ar] 4s2 3d4, but since this ends exactly with a d4 it is an exception to the rule. Thus, Cr should be [Ar] 4s1 3d5. Procedure: Find the closest s orbital. Steal one electron from it, and add it to the d.

Exceptions to the Aufbau Principle OK, so this helps the d, but what about the poor s orbital that loses an electron? Remember, half full is good… and when an s loses 1, it too becomes half full! So… having the s half full and the d half full is usually lower in energy than having the s full and the d to have one empty orbital.

Exceptions to the Aufbau Principle d9 is one electron short of being full Just like d4, one of the closest s electrons will go into the d, this time making it d10 instead of d9. For example: Au would be [Xe] 6s2 4f14 5d9, but since this ends exactly with a d9 it is an exception to the rule. Thus, Au should be [Xe] 6s1 4f14 5d10. Procedure: Same as before! Find the closest s orbital. Steal one electron from it, and add it to the d.

Orbitals fill in order Lowest energy to higher energy. Adding electrons can change the energy of the orbital. Half filled orbitals have a lower energy. Makes them more stable. Changes the filling order

Write these electron configurations Titanium(Ti) - 22 electrons 1s22s22p63s23p64s23d2 Vanadium(V) - 23 electrons 1s22s22p63s23p64s23d3 Chromium(Cr) - 24 electrons 1s22s22p63s23p64s23d4 is expected But this is wrong!!

Chromium is actually 1s22s22p63s23p64s13d5 Why? This gives us two half filled orbitals. Slightly lower in energy. The same principal applies to copper.

Copper’s electron configuration Copper has 29 electrons so we expect 1s22s22p63s23p64s23d9 But the actual configuration is 1s22s22p63s23p64s13d10 This gives one filled orbital and one half filled orbital. Remember these exceptions