1. 4.2b Quantum Numbers and Atomic Orbitals

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. The Schrodinger equation defines 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. The principal quantum number (n) designates the main energy levels n = 1, 2, 3, 4… Main energy levels are also called shells 1 2 3 4

5. The maximum number of electrons in each main energy level = 2n 2 (n = principal quantum number) 1 2 3 4

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.  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 1 2 3 4

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 any energy level?

9. 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. 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.  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. 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. 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. 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 sublevel (s, p) etc

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

17. Principal quantum number of n = 1 Only one sublevel (s) and s orbital has 2 electrons max So the first main energy level has 2 electrons max ( = 2n 2 )

18. 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 ( = 2n 2 )

19. 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 ( = 2n 2 )

20. 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 ( = 2n 2 )

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

22. Number of total orbitals at each main energy level: = n 2 n = 1 means there is only 1 total orbital (s)

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

25. How are these electron levels & sublevels organized within an atom?

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