Quantum Numbers

Quantum Numbers energy levels, size Pathway of travel Describes the arrangement of electrons in atoms in terms of: energy levels, size Pathway of travel Direction of rotation

Principal Quantum number (n) Contain electrons that are similar in energy and distance from nucleus Low energy electrons are closest to the nucleus Identify by numbers 1, 2, 3, 4, 5, 6….. The first shell (1) is lowest in energy, 2nd level next and so on 1<2<3<4

Number of Electrons Maximum number of electrons in any electron energy level = 2n2 n =1 2(1)2 = 2 n =2 2(2)2 = 8 n =3 2(3)2 = 18

Orbital Quantum number Indicates the pathway of travel Electrons move in different paths due to their negative charge. Designated s, p, d, f .. Sublevel energy: s<p<d<f

Magnetic Quantum number Orientation of path Direction of movement with respect to the nucleus

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

P orbitals 3 different directions 3 identical shapes Each can hold 2 electrons

P Orbitals put together

D orbitals Higher in energy than s or p due to advanced shape 5 shapes, 4 are identical

F orbitals More complex still Have seven different shapes

F orbitals More complex still

Spin Quantum number Describes rotation of electron in an orbital Either clockwise (+1/2) or Counter clockwise (-1/2)

Summary Seven energy levels (n=1,2,3,4…) Four pathways (s,p,d,f) Orientations: s=1, p=3, d=5, f=7 Two spins in each orbital Maximum electrons are: s=2, p=6, d=10, f=14

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

By Energy Level First Energy Level only s orbital only 2 electrons 1s2 Second Energy Level s and p orbitals are available 2 in s, 6 in p 2s22p6 8 total electrons

By Energy Level Third energy level s, p, and d orbitals 2 in s, 6 in p, and 10 in d 3s23p63d10 18 total electrons Fourth energy level s,p,d, and f orbitals 2 in s, 6 in p, 10 in d, ahd 14 in f 4s24p64d104f14 32 total electrons

By Energy Level Any more than the fourth and not all the orbitals will fill up. You simply run out of electrons The orbitals do not fill up in a neat order. The energy levels overlap Lowest energy fill first.

Electron Locations Main Energy Levels Sublevels n=4 4s, 4p, 4d, 4f

Sublevels in n = 1,2, 3 3d n = 3 3p 3s 2p n = 2 2s n = 1 1s

Electrons Allowed All electrons in the same sublevel have the same energy. All 2s electrons have the same energy. All 2p electrons, the same energy which is slightly higher than that of the 2s electrons s sublevel 2 electrons p sublevel 6 electrons d sublevel 10 electrons f sublevel 14 electrons

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

Electron Configurations List of subshells containing electrons Written in order of increasing energy Superscripts give the number of electrons

Electron Configuration Example: Neon number of electrons 1s2 2s2 2p6 main shell subshell

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

Electron Configuration Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to . Let’s determine the electron configuration for Phosporus Need to account for 15 electrons

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 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 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 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 5f14 6d10 7p6 108 electrons

Writing Electron Configurations H 1s1 He 1s2 Li 1s2 2s1 C 1s2 2s2 2p2 S 1s2 2s2 2p6 3s2 3p4

Periodic Table and Electron Configuration Find element on the periodic table Use the order of filling indicated across each period Groups 1-2 = ns level Groups 3-8 = np level Transition = (n-1)d level Lanthanides = (n-2)f level

Exceptions to Electron Configuration

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 - 22 electrons 1s22s22p63s23p64s23d2 Vanadium - 23 electrons 1s22s22p63s23p64s23d3 Chromium - 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. Write the Cu configuration now

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

Orbital Notation A 3 dimensional space around a nucleus in which electrons are most likely to be found Shape represents electron density (not a path the electron follows) Each orbital can hold up to 2 electrons.

Learning Check S5 A. Number of electrons in a p orbital 1) 1e 2) 1e or 2e 3) 3e B. Number of orbitals in a p subshell 1) 1 2) 2 3) 3 C. Number of orbitals in 4d subshell 1) 1 2) 3 3) 5 D. Number of electrons (maximum) in a 3d 1) 2e 2) 5e 3) 10e

Solution S5 A. Number of electrons in a p orbital 2) 1e or 2e B. Number of orbitals in a p subshell 3) 3 C. Number of orbitals in 4d subshell 3) 5 D. Number of electrons in a 3d subshell 3) 10e

The Periodic Law All the elements in a group have the same electron configuration in their outermost shells Example: Group 2 Be 2, 2 Mg 2, 8, 2 Ca 2, 2, 8, 2

Learning Check EA5 Specify if each pair has chemical properties that are similar (1) or not (2): A. Cl and Br B. 2 - 5 and 2 - 8 - 7 C. 2 - 4 and 2 - 8 - 4 D. P and S E. O and S

Solution EA5 Specify if each pair has chem. properties that are similar (1) or not similar (2): A. Cl and Br 1 B. 2 - 5 and 2 - 8 - 7 2 C. 2 - 4 and 2 - 8 - 4 1 D. P and S 2 E. O and S 1

Learning Check S2 Indicate if each configuration is (1) correct or (2) incorrect for potassium. Give an explanation for selection of 1 or 2. Explain A. 1s22s22p63s1 1 or 2 B. 1s22s22p63s23p6 1 or 2 C. 1s22s22p63s23p64s1 1 or 2 D. 1s22p83s1 1 or 2 E. 1s22s22p63s23p7 1 or 2

Solution E2 For phosphorus, indicate if each configuration is (1) correct or (2) incorrect. Explain why or why not. A. 2, 2, 8, 5 2 B. 2, 8, 3 2 C. 2, 8, 5 1 D. 2, 6, 7 2

Learning Check S3 Using the periodic table, write the complete electronic configuration for each: A. Cl B. Sr C. I

Solution S3 Using the periodic table, write the complete electronic configuration for each: A. Cl 1s2 2s2 2p6 3s2 3p5 B. Sr 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 C. I 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p5

Learning Check S4 A. The final two notations for Co are 1) 3p64s2 2) 4s24d7 3) 4s23d7 B. The final three notations for Sn are 1) 5s25p24d10 2) 5s24d105p2 3) 5s25d105p2

Solution S4 A. The final two notations for Co are 3) 4s2 3d7 B. The final three notations for Sn are 2) 5s2 4d10 5p2