of the Atom

Quantum Numbers and Orbitals

Werner Heisenberg and the uncertainty principle

De Broglie Vs Bohr

The quantum number, n, for a

hydrogen atom in its ground state is 1

principal quantum number, n

n: describes an orbital’s

energy level and size

orbital-shape quantum number l

l: describes an orbital’s shape

magnetic quantum number, m

The greatest number of electrons that is possible in any energy level is 2n

integer that ranges in value from 0 to (n − 1)

**Each value for l is given a letter: s, p, d, or f.**

• The l = 0 orbital has the letter s

• The l = 1 orbital has the letter p

• The l = 2 orbital has the letter d

• The l = 3 orbital has the letter f

• The l = 0 orbital has the letter s

• The l = 1 orbital has the letter p

• The l = 2 orbital has the letter d

• The l = 3 orbital has the letter f

**View what a full set of orbitals look like**

ex:

**Learning Check**

**sublevel with n = 3 and l = 1 is called the 3p sublevel**

**sublevel with n = 3 and l = 2 is called?**

is an integer with values ranging

from −l to +l, including 0

Learning Check

Problem:

(a) If n = 3, what are the allowed values for l and m , and what is the total number of orbitals in this energy level?

(b) What are the possible values for ml if n = 5 and l = 1? What kind of orbital is described by these quantum numbers? How many orbitals can be described by these quantum numbers?

If n = 3, l may be either 0, 1, or 2.

To find ml from l:

If l = 0, m = 0

If l = 1, m may be −1, 0, +1

If l = 2, m may be −2, −1, 0, +1, +2

Since there are a total of 9 possible values for ml, there are 9 orbitals

when n = 3.

l

l

l

l

l = 1, which describes a p orbital

Since n = 5, the quantum numbers represent a 5p orbital.

To find ml from l:

If l = 1, ml may be −1, 0, +1

Therefore, there are 3 possible 5p orbitals.

**spin quantum number,ms, and is given values of either 1/2 or 1/2.**

spin quantum number, m

s

Web

http://micro.magnet.fsu.edu/electromag/java/atomicorbitals/index.html

l

2

**sublevel with n = 2 and l = 2 is called?**

**(does not exist)**

**3d**