1. Unit 10: Atomic Theory and Periodicity
Section 2: Quantum Mechanical Theory

2. Problems with the Bohr Model
Suggests that orbiting electrons move at a specific radius, like a planet does around the sun
We later find out that oribtals are actually electron clouds, and differ in size, shape, and orientation
We use the quantum model to find the probability that an electron resides at a particular location
The denser the electron cloud, the higher the probability of finding an electron in that region

3. Quantum Numbers
Specifies the properties of atomic orbitals and the properties of electrons in orbitals
Each electron can be assigned a set of four quantum numbers
These numbers are the electron’s address

4. The First Quantum Number
Principal quantum number (n)
Describes the energy level
Are positive integers beginning with 1, 2, 3, etc.
The first energy level is closest to the nucleus, and each one after that moves farther away from the nucleus and increases in energy
More than one electron can
have the same energy level
The total number of orbitals
that exist is equal to n2
In energy level 1, there is only
1 orbital (12)
In energy level 2, there are 4
orbitals (22)

5. The Second Quantum Number
Angular momentum quantum number (l)
Describes the shape of the orbital as s, p, d, or f
s, p, d, and f are called energy sublevels
Has values from 0 to 3
s = 0
p = 1
d = 2
f = 3
At this level, we don’t go into
much detail with the “f” sublevel

6. The Second Quantum Number
s sublevel has one orbital, an s orbital
A capacity of two electrons
Makes up columns 1 and 2 on the p.t.
p sublevel has three orbitals, x, y, and z
A capacity of six electrons
Makes up columns 13 to 18 on the p.t.
d sublevel has five orbitals
A capacity of ten electrons
Makes up columns 3 to 12 on the p.t.
f sublevel has seven orbitals
A capacity of 14 electrons
Makes up the lanthanides and actinides on the p.t.

7. The Third Quantum Number
Magnetic quantum number (m)
Determines the orientation of an orbital around the nucleus
Has values ranging from –l through 0 to +l

8. The Fourth Quantum Number
Spin quantum number
Electrons are said to have either a +½ spin or a -½ spin
Also known as a clockwise and counterclockwise spin
Within an orbital, the first electron has a positive spin and the second electron has a negative spin
A single orbital can hold a maximum of two electrons, which must have opposite spin states

9. Quantum Number Relationships in Atomic Structure
Principal Quantum # (n)
Angular Momentum Quantum # (l)
# of orbitals per sublevel
# of orbitals per energy level
# of electrons per sublevel
# of electrons per energy level 1 s 2
2 and 3 4 8 p 3 6
4 and 5 9 18 d 5 10
6 and 7 16 32 f 7 14

10. Electron Configuration
A way of describing each of an element’s electrons
Written using the following steps:
Find out the # of electrons for the element
Start with the 1s part
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, etc.
For each orbital, insert the maximum # of electrons in the exponent position
Continue until each element’s electrons has been described
The superscripts should add up to the element’s atomic # (indicates # of electrons)

11. Electron Configuration Examples
The element sodium has 11 electrons
1s22s22p63s1
The sum of the superscript #s equal 11
= 11
The coefficients indicate the energy level and row # on the p.t.
The alphabet’s superscripts indicate the location and column # on the p.t.
The element silver has 47 electrons
1s22s22p63s23p64s23d104p65s24d9