Orbitals and Quantum Numbers

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Drill If the frequency of radiation is

4.68 x 10 -3 Hz. What is the wavelength of light in cm?

Objectives iWBAT Distinguish between the 4 quantum

numbers. 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.

Assign quantum numbers to specific electrons in atoms

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

Principal Quantum Number “n” The principal quantum number (n)

indicates the main energy level occupied by the electron

n can have integral values of 1, 2, 3, etc.

The Large Numbers Represent the Principal Quantum Numbers

http://www.angelo.edu/faculty/kboudrea/general/quantum_numbers/quantum_table1.gif

Principal Quantum Numbers

http://library.thinkquest.org/15567/lessons/sublevels.jpg

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

L is Mistral font

Which sublevel does each value of “l ” represent? Value of l letter used

0 s1 p2 d3 f

http://chemwiki.ucdavis.edu/@api/deki/files/4826/=Single_electron_orbitals.jpg

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/imgqua/hydco5.gif

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 NumberElectron 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, + ½ or - ½

http://www.brooklyn.cuny.edu/bc/ahp/LAD/C3/graphics/C3_quant_04.gifhttp://quantumanthropology2.files.wordpress.com/2012/04/picture-paul-40.png

Pauli Exclusion Principle 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

http://www.chemistryland.com/CHM130W/10-ModernAtom/Spectra/PeriodicTableWithQuantumNumbers.jpg

http://wps.prenhall.com/wps/media/objects/3081/3155040/blb0605/blb06t02.gif

http://atomicstructureforelectrons.webs.com/quantum-number-pic.gif

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?)

Can an e- be described by the following set of quantum numbers?

n=2, l=1, ml=-1All quantum numbers are allowed

values

Can an e- be described by the following set of quantum numbers?

n=1, l=1, ml=+1Not possible.The value of l must be less than the

valueof n.

Can an e- be described by the following set of quantum numbers?

n=7, l=3, ml=+3All the quantum numbers are

allowedvalues.

Can an e- be described by the following set of quantum numbers?

n=3, l=1, ml=-3Not 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=-2n=3, l=2, ml=+2n=4, l=3, ml=+3n=5, l=2, ml=+3

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