Download 4.2b Quantum Numbers and Orbitals File

4.2b
Quantum Numbers and Atomic Orbitals
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
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
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
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
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)?
POINT > Calculate number of electrons at different
principle energy levels
Maximum number of electrons in each main
energy level:
n = 1  2 electrons max.
4
n = 2  8 electrons max.
3
2
1
n = 3  18 electrons max.
n = 4  32 electrons max.
etc
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?
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
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)
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
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?
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)
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
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
WB CHECK :
How many sublevels in the third main energy level?
What are they?
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)
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)
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)
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)
WB CHECK :
The third main energy level (n = 3) has
a)
b)
c)
d)
three sublevels and 3 orbitals
three sublevels and 9 orbitals
three sublevels and 12 orbitals
one sublevel and 12 orbitals
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)
POINT > Determine number of orbitals at each main
energy level
Principal quantum number of n = 4
Should be 16 orbitals
s has 1 orbital
Max 16 orbitals
p has 3 orbitals
in n = 4
d has 5 orbitals
f has 7 orbitals
WB CHECK :
How many orbitals in the third main energy
level?
What are they?
How are these electron levels &
sublevels organized within atoms?
Homework:
Read pages 101-104
F.A. #1-3 page 104
#15-18 page 119