november 13, 2007

November 13, 20071. Please staple both labs together and place in basket.

a. Spectra lab 1st, Flame test 2nd

2. Then review by completing the following:1. Name the 4 orbitals2. Draw the 4 orbital shapes3. Define an orbital

3. Today in class, we will continue to describe electrons using the quantum mechanical model of the atom.

Homework: Important Dates:LEQ 11/29- Ch5 TestRead Ch5 11/26- E.C. due (pg 130)

Study Guide

Quantum Mechanical Model

From Bohr to present

6.5 Quantum Mechanical Atom• Electrons are outside the nucleus• Electrons can’t be just anywhere – occupy

regions of space• Knowing the location and energy of an

electron ( a wave) is limited in accuracy– Heisenberg Uncertainty Principle

• Orbitals– Regions in space where the electron is likely to be

found– Regions are described mathematically as waves

Schrodinger Wave EquationIn 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e-

Wave function (Y) describes:1 . energy of e- with a given Y2 . probability of finding e- in a volume of space

Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. Solutions to wave functions require integer quantum numbers n, l and ml.

7.5

• Solutions to wave functions require integer quantum numbers n, l and ml

• Quantum numbers are much like an address, a place where the electrons are likely to be found

Y = fn(n, l, ml, ms)

Each distinct set of 3 quantum numbers corresponds to an orbital

QUANTUM NUMBERSThe shape, size, and energy of each orbital is a function

of 3 quantum numbers which describe the location of an electron within an atom or ion

n (principal) ---> energy levell (angular momentum) ---> shape of orbitalml (magnetic) ---> designates a particular suborbital

The fourth quantum number is not derived from the wave function

s (spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½)

Schrodinger Wave EquationY = fn(n, l, ml, ms)

principal quantum number n

n = 1, 2, 3, 4, ….

n=1 n=2 n=3

7.6

distance of e- from the nucleus

e- density (1s orbital) falls off rapidly as distance from nucleus increases

Where 90% of thee- density is foundfor the 1s orbital

7.6

Y = fn(n, l, ml, ms)

angular momentum quantum number l

for a given value of n, l = 0, 1, 2, 3, … n-1

n = 1, l = 0n = 2, l = 0 or 1

n = 3, l = 0, 1, or 2

Shape of the “volume” of space that the e- occupies

l = 0 s orbitall = 1 p orbitall = 2 d orbitall = 3 f orbital

Schrodinger Wave Equation

7.6

Types of Orbitals (l)

s orbital p orbital d orbitall = 0 l = 2l = 1

l = 0 (s orbitals)

l = 1 (p orbitals)

7.6

p Orbitalsthis is a p sublevel

with 3 orbitalsThese are called x, y, and z

planar node

Typical p orbital

There is a PLANAR NODE thru the nucleus, which is an area of zero probability of finding an electron

3py orbital

p Orbitals

• The three p orbitals lie 90o apart in space

l = 2 (d sublevel with 5 orbitals)

7.6

d Orbitals

f OrbitalsFor l = 3 f sublevel with 7 orbitals

Y = fn(n, l, ml, ms)

magnetic quantum number ml

for a given value of lml = -l, …., 0, …. +l

orientation of the orbital in space

if l = 1 (p orbital), ml = -1, 0, or 1if l = 2 (d orbital), ml = -2, -1, 0, 1, or 2

Schrodinger Wave Equation

7.6

ml = -1 ml = 0 ml = 1

ml = -2 ml = -1 ml = 0 ml = 1 ml = 27.6

Y = fn(n, l, ml, ms)spin quantum number ms

ms = +½ or -½

Schrodinger Wave Equation

ms = -½ms = +½

7.6

Existence (and energy) of an electron in an atom is described by its unique wave function Y.

Pauli exclusion principle - no two electrons in an atomcan have the same four quantum numbers.

Schrodinger Wave EquationY = fn(n, l, ml, ms)

•Each seat is uniquely identified (E1, R12, S8)•Each seat can hold only one individual at a time

7.6

Schrodinger Wave EquationY = fn(n, l, ml, ms)

Shell – electrons with the same value of n

Subshell – electrons with the same values of n and l

Orbital – electrons with the same values of n, l, and ml

How many electrons can an orbital hold?

If n, l, and ml are fixed, then ms = ½ or - ½

Y = (n, l, ml, ½) or Y = (n, l, ml, -½)An orbital can hold 2 electrons 7.6

Summary• An electron has a 100% probability of being

somewhere• ORBITAL: The region in space where an electron is

likely to be found• The usual pictures of orbitals show the regions

where the electron will be found 90% of the time

http://www.falstad.com/qmatom/

7.6

Summary

How many 2p orbitals are there in an atom?

2p

n=2

l = 1

If l = 1, then ml = -1, 0, or +1

3 orbitals

How many electrons can be placed in the 3d subshell?

3d

n=3

l = 2

If l = 2, then ml = -2, -1, 0, +1, or +2

5 orbitals which can hold a total of 10 e-

7.6

Compare and contrast the Bohr and quantum mechanical models.

Summary