Orbitals and Quantum Numbers

Objective Students will be able to describe the quantum numbers n, l, and m l 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 3 quantum numbers: n, l, and m l

4 Quantum Numbers (reminder: quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals) 1) The principle quantum number (n) indicates the main energy level occupied by the electron n can have integral values of 1, 2, 3, etc.

2) 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

Value of lletter used 0s 1p 2d 3f

3) the magnetic quantum number (m l ) describes the orientation of the orbital in space It can take on values from l to –l

4) Electron Spin Quantum Number (m s ) 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, m l, and m s

Practice Problem 1) For n=4, what are the possible values of l ?

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

Practice Problem #2 For l =2, what are the possible values of m l ?

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

Practice Problem #3 State whether the following is a permissible set of quantum numbers for an electron in a hydrogen atom: n=2, l = 1, m l = 1

Answer Yes, it’s permissible (2p)