1. 4.2b Quantum Numbers and Atomic Orbitals
Atomic Structure

2. POINT > Describe the Principle Quantum number as an energy level
POINT > Calculate number of electrons at different main energy levels
POINT > Describe orbitals at each energy sublevel
POINT > Determine number of orbitals at each main energy level

3. POINT > Describe the Principle Quantum number as an energy level
The Schrodinger equations define the energy levels an electron can have
It also describes an atomic orbital as a region of space with a high probability of finding an electron

4. POINT > Describe the Principle Quantum number as an energy level
The principal quantum number (n) designates the main energy levels
n = 1, 2, 3, 4…
Main energy levels are also called shells 4 3 2 1

5. POINT > Describe the Principle Quantum number as an energy level
The maximum number of electrons in each main energy level =
2n2
(n = principal quantum number) 4 3 2 1

6. WB CHECK:
What is the maximum number of electrons in the first main energy level (n = 1)?
What is the maximum number of electrons in the fourth main energy level (n = 4)?
What is the maximum number of electrons in the third main energy level (n = 3)?
What is the maximum number of electrons in the second main energy level (n = 2)?

7. POINT > Calculate number of electrons at different principle energy levels
Maximum number of electrons in each main energy level: n = 1  2 electrons max. n = 2  8 electrons max. n = 3  18 electrons max. n = 4  32 electrons max. etc 4 3 2 1

8. OK…we know how many electrons can be in each main energy level, but…
How do we know more specifically where an electron is within an energy level?

9. POINT > Describe orbitals at each energy sublevel
For each main energy level (n), there may be several sublevels that describe more precisely where an electron is likely to be
Sublevel orbitals can have different shapes and different energy levels

10. POINT > Describe orbitals at each energy sublevel
Sublevels are labeled by letters (which correspond to numbers, l, the angular momentum quantum number)
s sublevel (l = 0)
p sublevel (l = 1)
d sublevel (l = 2)
f sublevel (l = 3)
Lower-case L

11. POINT > Describe orbitals at each energy sublevel
Maximum number of orbitals in each sublevel:
s sublevel (l = 0)  1 orbital
p sublevel (l = 1)  3 orbitals
d sublevel (l = 2)  5 orbitals
f sublevel (l = 3)  7 orbitals

12. WB CHECK:
How many d orbitals in one main energy level?
How many p orbitals in one main energy level?
How many s orbitals in one main energy level?

13. POINT > Describe orbitals at each energy sublevel
Every individual orbital can have a maximum of two electrons
If there are two electrons in an orbital, they must have opposite spin (spin quantum number)

14. POINT > Describe orbitals at each energy sublevel
Maximum number of electrons in each sublevel:
s sublevel (1 orbital)  2 electrons max
p sublevel (3 orbitals)  6 electrons max
d sublevel (5 orbitals)  10 electrons max
f sublevel (7 orbitals)  14 electrons max

15. POINT > Describe orbitals at each energy sublevel
Principal quantum number always equals the number of sublevels within that main energy level n = 1 means there can only be 1 sublevel (s) n = 2 means there can only be 2 sublevels (s, p) etc

16. WB CHECK :
How many sublevels in the third main energy level?
What are they?

17. POINT > Describe orbitals at each energy sublevel
Principal quantum number of n = 1
Only one sublevel (s)
one s orbital has 2 electrons max
So the first main energy level has 2 electrons max
( = 2n2)

18. POINT > Describe orbitals at each energy sublevel
Principal quantum number of n = 2
Two sublevels (s & p)
one s orbital has 2 electrons max and three p orbitals have 6 electrons max
So the second main energy level has 8 electrons max
( = 2n2)

19. POINT > Describe orbitals at each energy sublevel
Principal quantum number of n = 3
Three sublevels (s, p, & d)
one s orbital has 2 electrons max, three p orbitals have 6 electrons max, and five d orbitals have 10 electrons max
So the third main energy level has 18 electrons max
( = 2n2)

20. POINT > Describe orbitals at each energy sublevel
Principal quantum number of n = 4
Four sublevels (s, p, d, & f)
one s orbital has 2 electrons max, three p orbitals have 6 electrons max, five d orbitals have 10 electrons max and seven f orbitals have 14 electrons max
So the fourth main energy level has 32 electrons max
( = 2n2)

21. WB CHECK :
The third main energy level (n = 3) has
three sublevels and 3 orbitals
three sublevels and 9 orbitals
three sublevels and 12 orbitals
one sublevel and 12 orbitals

22. POINT > Determine number of orbitals at each main energy level
Number of total orbitals at each main energy level: = n2
n = 1 means there is only 1 total orbital (s)

23. POINT > Determine number of orbitals at each main energy level
Principal quantum number of n = 4 Should be 16 orbitals s has 1 orbital p has 3 orbitals d has 5 orbitals f has 7 orbitals
Max 16 orbitals
in n = 4

24. How many orbitals in the third main energy level?
WB CHECK :
How many orbitals in the third main energy level?
What are they?

25. How are these electron levels & sublevels organized within atoms?
Coming up:
How are these electron levels & sublevels organized within atoms?

26. Homework: Read pages 101-104 F.A. #1-3 page 104 #15-18 page 119