ELECTRONS IN ATOMS

Quantum Numbers, Orbitals,And Electron Configurations

Solving equations

• 3x = 15• One solution• X2 = 9• Two solutions• Schrodinger’s Equation• Infinite solutions

Schrodinger’s solutions

• An infinite number• Each is a set of four values• Called “quantum numbers”• n,l,m,s• In a given atom, each electron has a unique

set• This is that electron’s “address”

The First Quantum Number

• Principal quantum number n

• Values n = 1,2,3,….∞

• What it tells us: Orbital energy level Orbital size Number of nodes (n-1)

The Second Quantum Number

• Angular Momentum quantum number l

• Values l = 0, 1,2,3,… (n-1)

• What it tells us: Orbital energy sub-level Orbital shape Number of non-spherical nodes

Meaning of l values

• l=0 “s orbital” shape = spherical• l=1 “p orbital” shape = dumbbell• l=2 “d orbital” shape = double dumbbell• l=3 “f orbital” shape is more complex

The Third Quantum Number

• Magnetic quantum number m

• Values m = -l, … -1, 0, +1, …+l

• What it tells us: Orbital orientation (direction)

Possible m Values and Meanings

• This slide under construction…

• s orbitals occur singly• p orbitals occur in sets of 3• d orbitals occur in sets of 5• f orbitals occur in sets of 7

The Fourth Quantum Number

• Spin quantum number s

• Values – only two possible s = -1/2 or +1/2 Usually described as “up spin” or “down spin”

• What it tells us: The “spin” of an electron This is the only quantum number that describes a

particle aspect of the electron

Probability Distributions

• What is the electron doing in the orbital? We don't know, and we can't know, and so we just ignore the problem! All you can say is that if an electron is in a particular orbital it will have a particular definable energy.

• http://www.chemguide.co.uk/atoms/properties/atomorbs.html (and following slide visuals:)

Probability distributions for s orbitals

Probability distributions for p orbitals

The Credit:

• The link below has excellent visuals of many of the orbitals. Much of the wording on the following slides is copied directly from this (“ORBITRON”) site.

• http://winter.group.shef.ac.uk/orbitron/

1s orbital

• For any atom there is just one 1s orbital. Consider the shape on the left. The surface of the shape represents points for which the electron density for that orbital is the same - an isosurface. The image shows clearly the spherical shape of the 1s function.

• http://winter.group.shef.ac.uk/orbitron/AOs/1s/index.html

2s orbital

• For any atom there is just one 2s orbital. • The image on the left is deceptively simple as the

interesting feature is buried within the orbital. That on the right is sliced in half to show that there is a spherical node in the 2s orbital.

• While still spherical, the higher s-orbitals (3s, 4s, 5s, 6s, and 7s) are more complex since they have more spherical nodes.

• http://winter.group.shef.ac.uk/orbitron/AOs/2s/index.html

2p orbitals -- NOT

• It is common to denote the shapes of 2p orbitals … as shown below. These "figure-of-eight" style pictures … make the orbitals appear much "thinner" than they are really, and also that there are sharp "points" in the region of the nucleus, which there are not.

2p orbitals• For any atom, there are three 2p orbitals. These orbitals have the same

shape but are aligned differently in space. The three 2p orbitals normally used are labelled 2px, 2py, and 2pz since the functions are "aligned" along the x, y, and z axes respectively.

• Each 2p orbital has two lobes. There is a planar node normal to the axis of the orbital (so the 2px orbital has a yz nodal plane, for instance). The higher p-orbitals (3p, 4p, 5p, 6p, and 7p) are more complex still since they have spherical nodes as well.

• The origin of the planar node becomes clear if we examine the wave equation which, for instance, includes an x term in the case of the 2px orbital. Clearly When x = 0, then we must have a node, and this by definition is the yz plane.

• http://winter.group.shef.ac.uk/orbitron/AOs/2p/index.html

3p, 6p, 7p

• http://winter.group.shef.ac.uk/orbitron/AOs/3p/index.html

• http://winter.group.shef.ac.uk/orbitron/AOs/6p/index.html

• http://winter.group.shef.ac.uk/orbitron/AOs/7p/index.html

3d orbitals

• For each atom, there are five 3d orbitals. These are labelled 3dxy, 3dxz, 3dyz, 3dx

2-y

2 and 3dz2. Four of these

functions have the same shape but are aligned differently in space. The fifth function (3dz

2) has a different shape.

• Each 3dxy, 3dxz, 3dyz, and 3dx2

-y2 orbital has four lobes. There

are two planar node normal to the axis of the orbital (so the 3dxy orbital has yz and xz nodal planes, for instance). The 3dz

2 orbital is different and has two conical nodes.

• http://winter.group.shef.ac.uk/orbitron/AOs/3d/index.html

• The higher d-orbitals (4d, 5d, and 6d) are more complex since they have some spherical nodes.

• http://winter.group.shef.ac.uk/orbitron/AOs/4d/index.html

• http://winter.group.shef.ac.uk/orbitron/AOs/6d/index.html

• http://winter.group.shef.ac.uk/orbitron/AOs/7d/index.html

4f orbitals

• For any atom, there are seven 4f orbitals. The f-orbitals are unusual in that there are two sets of orbitals in common use. Those shown here are the cubic set . … The other set is known as the general set.

• http://winter.group.shef.ac.uk/orbitron/AOs/4f/index.html

Orbital Filling Game

• http://www.learner.org/interactives/periodic/elementary2.html

Another good reference

• http://antoine.frostburg.edu/chem/senese/101/electrons/