Transcript Document

Hot Topics in Physics:
The Basics of Matter
A Conceptual Overview of How
Matter Behaves Leading up to
Chemistry
Originally Presented at Mesa Community College
November 6, 2013
Some physics questions
Suppose that a ball is rolling along a flat surface. In 10
seconds it goes 5 feet. How far would you expect it to
travel over the next 10 seconds?
With no interference, another 5 feet
A falling object drops 16 feet in one second. In the next
second would you expect it to fall more, less or the
same amount?
More than 16 feet
In science we seek to understand and make sense of
the world around us.
We like to have things predicable, or even mechanical.
When it comes to understanding the matter that
makes up everything around us, we need to focus on
the building blocks. This means dealing with atoms
and their components.
When we talk about atoms we must first begin with
what makes up an atom.
Central part, called the
nucleus. This is where almost
all the mass is. The nucleus
holds the atom together.
Tiny electrons buzz around the
nucleus, filling in most of the
space.
Overlapping electrons from neighboring atoms trap
the atoms together.
When atoms are trapped together
we say that there is a Bond between
them.
So understanding how atoms bond
together means understanding
electrons.
But there are two big complications!
First: At the basic level matter shares
the same level of predictability as
people.
One person is difficult or to impossible
to predict in terms of future behavior.
Groups of people are much easier to
predict.
No problem, we just look for trends of
behavior or chances that certain types
of behavior will occur.
This leads to complication #2
The ordinary way we go about determining the
chances of different outcomes is different for matter
at the basic level than it is for our everyday world.
Example: Suppose that one shots blasts from a single or double-barrel
shotgun at a target. We would expect to see patterns similar to these.
Single Barrel
Double Barrel
If we imagine a strange shotgun where the shot from a single cartridge gets
divided up between two barrels, the pattern should be similar.
Now apply that same logic to a beam containing electrons, atoms and so forth.
Target
Beam
hits
target
via 2
routes
Split it up
This looks like the shotgun scenario, so we should have a similar outcome.
Source
However…. This is not always what we see in reality
We could see our familiar friend ..
Or if we simply adjust the speed of the
matter being examined we can see
something new.
or
A real example: Shooting electrons through
a powdered crystal
We need to adjust our thought process to give us
wiggle-room for the different outcomes.
We give ourselves the needed wiggle-room by working with what are
called
Probability Amplitudes
Simply put, instead of talking about the chances for a certain
outcome to occur, we work with numbers that, when squared, gives
us the chance for the outcome.
Here is how the game is played: An example
What is the chance that, if you roll a die, you will roll a 5?
1 possible way to get 5
6 total possible outcomes
What is the chance that, if you roll a die, you will roll a 4?
What is the chance that, if you roll a die, you will roll a 4 or 5?
This tells us to expect a roll of a 4 or 5, on average, once every 3 rolls.
How do you play the game with Probability Amplitudes?
What is the probability amplitude that, if you roll a die, you will roll a 5?
What is the probability amplitude that, if you roll a die, you will roll a 4?
What is the chance that, if you roll a die, you will roll a 4 or 5?
We have two possible answers, depending on whether we add or subtract the numbers.
Using amplitudes gives us wiggle room to resolve our problem. In fact probability
amplitudes can also be complex numbers, giving added flexibility.
Working through the mathematics of Probability Amplitudes is the business of
Quantum Mechanics.
The mathematics can be formidable.
For example when the equations are applied to the electron in a
Hydrogen atom one gets equations like these.
Schrodinger Equation:
Dirac Equation:
Don’t Panic, Remain calm
All that we are interested in as far as the math goes is that it
produces a family of equations. Without worrying about the
exact details of these equations we will consider the
consequences.
As with any family, we need a way to distinguish one member from another.
For our equation family, this
means introducing a set of
numbers called Quantum
Numbers.
n, l, ml
Also it is convenient to include a 4th Quantum Number, ms
So what values can n, l, ml and ms have?
• n can be any natural number: 1, 2, 3, …
• l can be any whole number less than n: 0, 1, 2, … n-1
Example: If n = 5 then l can equal 0, 1, 2, 3 or 4
• ml can be any integer between –l and +l
Example: If l = 3 then ml can equal -3, -2, -1, 0, 1, 2 or 3
• ms can only be - ½ or + ½
So let us summarize where we’ve been
• Matter is fundamentally unpredictable. We need to devise new rules
to predict the chances of different outcomes being realized.
• We deal in “probability amplitudes.” The equations dealing with these
can turn out to be nasty.
• When applied to a Hydrogen atom we get a family of solutions
distinguished by a set of four “quantum numbers,” n, l, ml, ms.
• Historically the results for Hydrogen have been generalized to describe
the electrons in atoms with multiple electrons.
So what has all this bought us?
We cannot predict where an electron for an atom is located, so let us suppose that
we did countless experiments measuring where electrons are and plotted them.
What might we see?
Consider the case where n = 1, l = 0, ml = 0 and ms = ± ½
We see that the electrons will tend to be found grouped around the nucleus.
While we cannot tell where the electron will be, and so cannot define its path as
an orbit, we can describe the region it is most likely to located as an orbital.
For all solutions where l = 0 the convenient region is just a spherical region
called an s-orbital.
How about the other solutions? Consider the cases where:
l = 1, ml = 0 and ms = ± ½
l = 1, ml = ± 1 and ms = ± ½
For the ml = 0 case we see that the electrons tend to group in
clusters on either side of the nucleus.
For the ml = ± 1 case the electrons form a doughnut type shape
around the nucleus. This is no good for atoms with multiple
electrons as it would tend to put them too close together.
However if we add or subtract them we get the same clustering
in perpendicular directions.
So for the three l = 1 solutions we also have orbitals. Only now it is 3
dumbbell shaped orbitals in perpendicular directions.
We can keep this up ad nauseum. However the pattern is already
beginning to form. Each l value has a set of orbital(s) describing the
most possible locations to find the electron.
l = 0 (one s orbital) ml = 0
l = 1 (3 p orbitals) ml = -1, 0, 1
l = 2 (5 d orbitals) ml = -2, -1, 0, 1, 2
But how does all this relate to the
arrangement of atoms in a molecule?
Remember that atoms bond via the sharing of electrons. The atoms
must be arranged to reflect where the electrons are. These are where
the orbitals are.
Example: Hydrogen molecule (Two 1s orbitals)
Example: Chlorine molecule (Two 3p orbitals)
In our previous examples we saw molecules in nice straight
lines where only one pair of electrons being shared.
Yet often times our previous arrangement does not work, the
electrons will try to spread themselves out more than is
permitted by the orbitals we have developed.
Example: Methane (The carbon’s 2p orbitals cannot account for this)
The problem is that we generalized our results for a
hydrogen atom (one electron) to all atoms. The solution
is to mix around the existing orbitals into a new group of
orbitals called Hybrid Orbitals.
The end result is that we have a set of orbitals that
allow for atoms to be arranged such that the
electrons are spread out as far from each other as
possible.
Example: Linear (CO2)
Example: Trigonal planar (BCl3)
Example: Trigonal pyramidal (NH3 – Nitrogen has two unseen pairs of electrons)
One other aspect an electron in an atom is its
energy.
Energy, like any aspect of matter in a Quantum
World, is not always predictable.
However our family of solutions is built under the
basis that energy is fixed, with values that would
repeatedly be found in an actual measurement.
What this indicates that the electron is viewed as
being restricted to the energy values allowed it by
the family of solutions. These values are called
Energy Levels.
When an electron gives off light it does so by going
from one energy level to another.
This means that the wavelengths of light that are
given off are restricted to a set of possibilities.
Full spectrum
Empirical
Examples:
Hydrogen
Helium
Let us return to our earlier Physics question.
Suppose that a ball is rolling along a flat surface. In 10
seconds it goes 5 feet. How far would you expect it to travel
over the next 10 seconds?
How can we incorporate what we have seen to this
question?
• We cannot guarantee that we will know will it
will be. But we can use probability amplitudes
to determine the likelihood of it being found in
different locations.
• The probability amplitudes must be able to shift
how they are distributed.
In order to allow amplitudes to shift around they
must be viewable as quantities can that move
about.
These movable amplitudes are describable as
waves.
Usually matter itself gets described as a wave itself.
This marriage of convenience where matter is
considered as a mixture of particle properties with
wave properties is called wave-particle duality.
The core idea between the wave-particle philosophy:
• Prior to taking a measurement, one can view
matter as being a wave.
• At the point of measurement the matter
becomes a particle.
Thank-You!!