Quantum Numbers SCH4U1 Mr. Dvorsky

-We cannot determine the exact location of an electron. -With Schrodinger’s wave equation we can define a 3D area of space around the nucleus where an individual electron is likely to be found. -We can describe this area using a set of 4 quantum numbers. This is like the home address of an electron.

Principal Quantum Number (n) Recall that the Bohr model had energy levels (or shells). We still have energy levels or shells in the quantum mechanical model, and they are described by the principal quantum number n, =1, 2, 3, etc.

As n increases, the energy required by an electron to occupy that level increases Also, successive orbitals are larger, so larger n = bigger orbitals So… The Principal Quantum number describes the energy and size of an atomic orbital.

-the energy between atomic shells is not equal (i. e -the energy between atomic shells is not equal (i.e. some of the gaps are larger than others)

Secondary Quantum Number, l

With improved technology it became apparent that Bohr’s energy levels or shells were actually composed of subshells That is to say at any energy level n, there are different types of orbitals that have small differences in energy These different types of orbitals have different shapes. The second quantum number, l, describes the shape.

The value for l ranges for 0 to n-1. So for n =1, l =0 For n =2, l = 0, 1 For n = 3, l = Each value for l is assigned a corresponding shape. l = 0 (code name sharp), abbreviated s. l = 1 (code name principal), abbreviated p. l = 2 (code name diffuse), abbreviated d. l = 3 (code name fundamental), abbreviated f. s is spherical shape, p is dumbbell shaped, d and f have shapes that are more difficult to describe with words.

So at energy level 3 for example, you have l = 0, 1, 2 - therefore at that energy level you have orbitals that are s shaped, p shaped, and d shaped. Each of these shapes is a subshell, they differ slightly in energy (the little stairs inside the big stairs).

The magnetic quantum number, ml Describes the orientation of the orbital in space relative to the other orbitals In other words, there is more than one way that you can arrange a dumbbell in space. Each shape has a possible number of orientations that ranges from +l to –l including 0. See table 2 on page 155, figure 5 156

Recap: 3py

The Spin Quantum Number, ms An electron can spin in two possible directions. Each spin causes a slightly different band on the emission spectra for an atom. The two possible spin directions are designated as being either +1/2 or -1/2

The Pauli Exclusion Principal In a given atom, no two electrons can have the same set of 4 quantum numbers. Since each orbital can hold two electrons, each must have opposite spin therefore the two electrons in the same orbital differ in the 4th quantum number.