Quantum numbers
Where Does Tin-Tin Live?
http://www.epa.gov/kidshometour/images/house.jpg
Where Does Tin-Tin Live?
Tin-Tin lives in a dorm in a condominium unit. In
the dorm, there are male and female sections
per floor. Per room, there are only two beds. If
asked where EXACTLY she lives, how would
she answer?
Prince David Condominium in Katipunan Ave
3rd floor
Female section
Room 314
Bed near window
The quantum mechanical model answers the
question, “Where does the electron live?”
Prince David Condominium
in Katipunan Ave
The electron belongs to
chlorine
3rd floor
3rd energy level (n=3)
Female section
In the p-subshell (l=1)
Room 314
In one of the three
degenerate orbitals
eg. ml= 0
Bed near window
Electron is spin-up
eg. ms= +1/2
The quantum mechanical model answers the
question, “Where does the electron live?”
•
•
Three quantum numbers describe the
electron’s address
1. principal quantum number (n)
2. angular momentum quantum number (l)
3. magnetic quantum number (ml)
A fourth quantum number is added to pinpoint
the location
4. spin quantum number (ms)
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
The principal quantum number (n) gives the
distance of the e- from the nucleus
n=3
n=1
n=2
n = 1, 2, 3, 4, ….
The larger the n, the larger
the average distance of the
e- from the nucleus
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
The values of the angular momentum
quantum number (l) depend on n
for a given value of n, l = 0, 1, 2, 3, … n-1
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
The values of the angular momentum
quantum number (l) depend on n
Silberberg, M. 2010. Principles of General Chemistry. 2nd ed. New York: McGraw-Hill.
The angular momentum quantum number (l)
gives the shape of the orbital
l
0
1
2
3
Name
of
Orbital
s
p
d
f
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
The angular momentum quantum number (l)
gives the shape of the orbital
l=0
s orbital
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
The angular momentum quantum number (l)
gives the shape of the orbital
l=1
p orbital
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
The angular momentum quantum number (l)
gives the shape of the orbital
l=2
d orbital
Silberberg, M. 2010. Principles of General Chemistry. 2nd ed. New York: McGraw-Hill.
The angular momentum quantum number (l)
gives the shape of the orbital
l=3
f orbital
http://int.ch.liv.ac.uk/Lanthanide/Graphics/f-orbs.gif
The value of the magnetic quantum number (ml)
depends on l
for a given value of l, ml = l, …., 0, …. -l
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
Silberberg, M. 2010. Principles of General Chemistry. 2nd ed. New York: McGraw-Hill.
The magnetic quantum number (ml) describes
the orientation of the orbital in space
ml = +1
ml = 0
ml = -1
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
The spin quantum number (ms) accounts for
an electron’s ability to act like tiny magnets
ms = +½
ms = -½
Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill.
Terms to remember
• Shell
– electrons with the same values of n
• Subshell
– electrons with the same values of n and l
• Orbital
– electrons with the same values of n, l, and
ml
– an orbital can hold at most two electrons
Note that the orbitals are just spaces—it
does not mean that an electron occupies the
entire space at any given time
Test Your Understanding
• For n = 4, what are the possible
combinations of l and ml?
l=0
l=2
ml = 0
ml = -2, -1, 0, +1, +2
l=1
l=3
ml = -1, 0, +1
ml = -3, -2, -1, 0, +1, +2, +3
Test Your Understanding
Which of the following are permissible sets
of quantum numbers for an electron (n, l,
ml)? If permissible, write the subshell to
which it belongs
1. (2, 2, -2)
Not permissible
2. (4, 3, -1)
Permissible, 4f
3. (1, 0, 0)
Permissible, 1s
4. (6, 3, -4)
Not permissible