Orbitals and Quantum Numbers (rev. 12/04/08)

Objective Students will be able to describe the quantum numbers n, l, and ml used to define an orbital in an atom, and list the limitations placed on the values each may have.

What is an orbital? An orbital is an allowed energy state of an electron in the quantum-mechanical model of the atom; the term orbital is also used to describe the spatial distribution of the electron. Defined by the values of 4 quantum numbers: n, l, and ml , ms

4 Quantum Numbers Reminder: quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals)

Principle Quantum Number “n” The principle quantum number (n) indicates the main energy level occupied by the electron n can have integral values of 1, 2, 3, etc.

Azimuthal Quantum Number The angular momentum (or azimuthal) quantum number (symbolized by “l “) indicates the shape of the orbital “l “ can take on integral values from 0 to n -1 for each value of n

Which sublevel does each value of “l” represent? Value of l letter used 0 s 1 p 2 d 3 f

Magnetic Quantum Number The magnetic quantum number (ml) describes the orientation of the orbital in space It can take on values from “l to –l” For example: If “l” is 2 then ml could be 2, 1, 0, -1, -2

Electron Spin Quantum Number Electron Spin Quantum Number (ms) This number indicates the two fundamental spin states of an electron in an orbital This quantum number can only have two possible values, +1/2 or -1/2

Pauli Exclusion Principle – states that no two electrons in an atom can have the same set of 4 quantum numbers n, l, ml, and ms

Practice Problem #1 For n=4, what are the possible values of l ? Answer on next slide.

Answer l = 0,1,2,3 (what do these values correspond to?)

Practice Problem #2 For l =2, what are the possible values of ml ? Answer on next slide.

Answer ml = 2,1,0,-1,-2 (what do these values correspond to?)

Problems to try Brown & LeMay P. 222 problems 60, 61, 62

Can an e- be described by the following set of quantum numbers? n=2, l=1, ml=-1 All quantum numbers are allowed values

Can an e- be described by the following set of quantum numbers? n=1, l=1, ml=+1 Not possible. The value of l must be less than the value of n.

Can an e- be described by the following set of quantum numbers? n=7, l=3, ml=+3 All the quantum numbers are allowed values.

Can an e- be described by the following set of quantum numbers? n=3, l=1, ml=-3 Not possible. The value of ml must be in the range -l to +l

Can an e- be described by the following set of quantum numbers? n=2, l=1, ml=-2 n=3, l=2, ml=+2 n=4, l=3, ml=+3 n=5, l=2, ml=+3

Replace the ? Mark with an appropriate quantum number. n=3, l=1, ml=? n=4, l=?, ml=-2 n=?, l=3, ml=?