Lesson 18 Quantum Numbers and Electron Configurations

Objectives:

-         1. The student will define and explain the four quantum numbers.

-         2. The student will explain and apply Hund’s Rule and the Pauli Exclusion Principle.

-         3. The student will write electron configurations for elements, as well as determine what element is represented by a specific electron configuration.

I. Scientists whose theories led to the understanding of the electron:a. Louis deBroglie: French graduate student in physics

who proposed The DeBroglie Hypothes, which states that particles have properties of waves as well as properties of particles, “the wave particle duality of nature” Formula ( λ= h/mv ) λ=wavelength, h= Planck’s constant, m= mass in kg, v= velocity in m/s

b. Werner Heisenberg: German physicist who published the Heisenberg Uncertainty Principle: it is impossible to know the exact location and exact momentum of a particle at the same time.

c. Erwin Schrodinger: 1926, Austrian physicist who treated electrons as waves to help determine probability of location within an atom. This led to the creation of the quantum mechanical model that we use to explain the structure of the atom today.

II.  Labeling Electrons in atoms

a.      Quantum numbers are used to differentiate between electrons

                     i.      In quantum theory, each electron in an atom is assigned a set of four quantum numbers.

                     ii.      Three of these give the location of the electron, and the fourth gives the orientation of the electron within the orbital

                     iii.     Definitions of numbers

` 1.      Principle Quantum Number – n – This number describes the energy level that the electron occupies. It can have a value of 1-7 – This defines the “level” of the electron.

2.      Orbital Quantum Number – l – (Azimuthal) this number describes the shape of the orbital that the electron is found in. It can have a value from 0-3. This defines the “sublevel” of the electron. Also, the numbers can be replaced by letters according to the following:

a.       0 = sb.      1 = pc.       2 = dd.      3 = ff orbital shapes:

3.      Magnetic Quantum Number - ml – this number

describes the orientation of the electrons in the orbitals. This defines the “orbital” of the electron. There are 2l+1 orbitals in each sublevel. This quantum number can have the following values: (-l to +l)

a.       If l = 0, ml can equal 0

b.      If l = 1, ml can equal –1, 0, +1

c.       If l = 2, ml can equal –2, -1, 0, +1, +2

d.      If l = 3, ml can equal –3, -2, -1, 0, +1, +2, +3

4.      Spin Quantum Number – ms – this number describes the

direction of spin of the electron in the orbital – electrons in the same level and sublevel must spin in opposite directions. This can have a value or +1/2 or –1/2 only.

iv.      According to the Pauli Exclusion Principle, no two electrons can have the same four quantum numbers in the same atom.

v.      Think of these as City, Street, House Number, and upstairs/downstairs apartment. No two people could have the same complete address, but they could live in the same city, on the same street, or even in the same house, but not the same apartment.

b. Orbital diagrams and electron configurations are models for electron arrangements.

              i.      Orbital diagrams are used to show how electrons are distributed among the different sublevels and also to show the direction of spin.

            ii.      For orbital diagrams, you must fill in orbitals in

the same energy level with one electron each before pairing up any electrons. This is known as Hund’s Rule.

            iii.      Electron configurations are used to show similar information, but are a much more abbreviated form.

            iv.      How many electrons can go in any level?

(Maximum)1.      s = 22.      p = 63.      d = 104.      f = 14

                v.     What order do I fill the levels in? The Aufbau Principle states that when predicting an atoms ground state electron configuration, electrons will occupy the lowest energy orbital available first.

 1s

2s 2p  3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f

6s 6p 6d

7s 7pvii.      This also could be written: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s,

4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

c. Electron configurations can be written in terms of noble gases

i. Instead of writing out the long configurations that some of the larger elements would have, you can abbreviate by using the next smallest noble gas to the element in question to replace most of the electron configuration.

ii. Only noble gases can be used for this. Don’t replace part of an electron configuration with any other element.

iii. Example Configurations with the noble gas shortcut:1. Cl

2. W

3. Ra

4. K

5. Zn

6. At

7. Cf

III. Writing Lewis Structures or Lewis Dot Diagrams for elements

a. This is a kind of short hand that illustrates how many outer shell electrons an atom contains.

b. The purpose behind all of the configurations is because the number of electrons and their placement in the atom, strongly influences how the atom will react, bond and the properties it will demonstrate.

c. Rules for writing dot diagrams:i. Write configuration.

ii. How many e- are in the outer energy level?

iii. Write the elements symbol.

iv. Draw dots around the symbol to represent outer level electrons, each of the 4 sides represents an orbital.

v. “s” electrons must be paired (1st two e-)

vi. Other three sides cannot be paired until each has at least one e-. (Hund’s Rule)

d. Example:

e. Dot diagram examples:

i. C

ii. Br

iii. Ar

iv. H

v. Mg

vi. Ag

vii. P

viii. O

IV. Exceptions to electron configuration using the Aufbau Diagram

a. A half full level is the next stable thing to a full level.

b. Some atoms will violate our predictions in order to achieve stability. This can occur in the transition metals when the predicted configuration ends in a d4 or d9.

c. It will steal a single electron from the full s shell that came before it to obtain 2 half full shells or one half and one full shell.

d. (s2 d4) becomes (s1 d5) and (s2 d9) becomes (s1 d10)

e. Actual exceptions:* 5d1 fills before starting the 4f sequence* 6d1 fills before starting the 5f sequence

Predicted configurations Actual configurations

Cr:[Ar]4s2, 3d4 Cr:[Ar] 4s1, 3d5Cu:[Ar] 4s2, 3d9 Cu[Ar] 4s1, 3d10 Nb:[Kr]5s2,4d3 Nb:[Kr] 5s1, 4d4Mo:[Kr] 5s2, 4d4 Mo[Kr] 5s1, 4d5Tc:[Kr] 5s2, 4d5 Tc[Kr] 5s1, 4d6Ru[Kr] 5s2, 4d6 Ru[Kr] 5s1, 4d7Rh[Kr] 5s2, 4d7 Rh[Kr] 5s1, 4d8Pd[Kr] 5s2, 4d8 Pd[Kr] 5s0, 4d10Ag[Kr] 5s2, 4d9 Ag[Kr] 5s1, 4d10Pt[Xe] 6s2, 4f14, 5d8 Pt[Xe]6s1, 4f14, 5d9Au[Xe] 6s2, 4f14, 5d9 Au[Xe] 6s1, 4f14, 5d10

Questions:

1. Make a chart, with the following columns: Quantum number name, symbol, possible values. Fill in the information for each of the four quantum numbers.

2. What is the reason that an element cannot have all four quantum numbers the same?

3. What is the rule which means “spread them out before you pair them up”?