Download Quantum physics

Quantum physics
Comes from idea that physical quantities are
discontinuous or quantized.
Examples: charge comes in quantities of 1.6x10-19 C
All electric charges are some integer multiples of 1.6x10-19 C
Let’s call 1.6x10-19C = e
Allowed charges are: 1.6x10-19C, 3.2x10-19C, 4.8x10-19C…
or 1e, 2e, 3e, 4e, …
Cannot have: 1.5e or 2.1x10-19C
More examples of quantization
• Light occurs is packets called photons. If you
dimmed a light bulb enough you could release
light, 1 photon at a time.
Photons will be further discussed later.
• Electrons that orbit the nucleus have discrete
(quantized) energies.
The Waviness of matter.
Louis de Broglie thought that radiation, such
as light, could behave as a wave and as a
particle, then particles should behave like
waves.
Came up with a formula to predict the
wavelength of a material particle.
wavelength of particle = h/(mass*velocity)
Wavelength of a 1 kg ball rolling 1 m/s
6.6 x10 34 J s
(1kg)(1m / s )
6.6 x10
34
m
This number is very small. Too small to detect.
Wavelength of an electron moving with a typical
velocity of 107 m/s.
6.6 x10 34 J s
(9.1x10 31 kg)(10 7 m / s )
7 x10
11
m
Still very small. About 1/10 the size of an atom.
Can be detected by very careful experiments.
For ‘big’ objects, anything of noticeable size, the
wavelength of the object is amazingly small.
The object needs to be very small for its wavelength to be
detectable.
Quantum physics is more useful at the microscopic level.
Quantum mechanics accurately describes the behavior of
particles such as electrons and atoms. For larger objects,
such as people, the quantum mechanics breaks down to
classical mechanics (The rules of physics that we’re use to
using.)
Turns out that energy in an electric-magnetic field
does not come in a continuous values. It is quantized.
EM fields that oscillate produce light waves. The energy in these
waves is quantized.
The amount of energy in the field can only have certain
values.
These energy values are = 0, hf, 2hf, 3hf, 4hf, …
h = Planck’s constant = 6.6x10-34 J*s
f is the frequency
Remember that v=f or f = c/
Thus the values of energy can be written as:
0, h c/ , 2hc/ , 3hc/ , 4hc/ , …
•
•
•
•
Photons are the quanta (carriers of the quantized energy).
The photon will have an amount of energy of Planck’s constant
times the frequency of the photon.
E=hf
Different colors have different wavelengths.
Wavelength is related to frequency by f = c/ or =c/f
So different colors have photons of different energies.
Photons only exist at the instant of impact between light and
an object.
When a photon hits a screen and causes it to light up, the
entire EM field loses an amount of energy equal to the energy
of the photon.
This is how light interacts with matter.
Light, a wave, sometimes interacts with matter like a particle.
To explain how Electromagnetic waves (light) are
produced, we first discuss the electron.
Quantum theory of the atom describes the behavior of
electrons.
Electrons can described to follow the rules of standing
waves. (Show standing waves with long spring.)
Notice the number of loop/nodes/humps are
quantized. This means the wavelength and frequencies
are quantized. Thus the energies of the electrons are
quantized.
The more loops that are present, the lower the
wavelength or higher the frequency. This means
higher energy.
Electron waves are similar, but bent into a
circle. See pictures on page 342, 343.
Each frequency corresponds to a quantum
state. The quantum states have their own
energy level.
The lowest energy level is called the ground
state.
Higher energy levels are excited states. They
are more energetic than the ground state.
Energy level diagram
Shows the quantized energy levels that the
electrons are allowed to exist in. This will be
determined by the type of atom.
The energy of the electrons is quantized. For an
electron to change energies, it must jump from
one state to another.
Emission
When an electron falls from a higher level to a
lower level, a photon is emitted. The photon will
have energy equal to the difference in the
quantum jump. The atom gives off light.
The change in the energy levels is equal to the
energy of the photon is E = hf
(note: quite often we use a new energy unit called the
electron-volt, eV. It’s more convenient than the Joule because
the energies dealt with are small)
Absorption
Atoms can absorb light (photons). If a photon
hits an atom and it’s energy matches the
change in energy between electron energy
levels, the photon is captured by the atom. To
“make room” for the energy, and electron is
bumped up to a higher level.
This process is the opposite of emission.
Since the energy levels that the electrons can
occupy are quantized, it means that only
certain frequency photons can be emitted or
absorbed.
The energy levels depend on the atom.
So different atoms emit/absorb different
colored photons. (different wavelengths).
spectroscopy – by looking to see the wavelengths
of the emitted/absorbed photons, you can
determine what material is made out of.
Knowledge about atomic spectra can be very
useful in some situations.
By looking at the radiation of a distant star, you can
determine what gases are in the star.
Or let’s pretend you want to have a light source
that produces only specific colors:
You can decide what type of gas lamp to use.
This is also related to making lasers. By exciting
electrons to different energy levels, we can make
lasers that produce different colors.
Spectrum
spectrum – set of frequencies that are emitted/absorbed
White light has a continuous spectrum. White light is
made up of all the colors.
line spectrum – produced when only precise separated
frequencies are emitted. Two types:
Emission spectrum – shows the wavelengths that are
emitted in form of lines on the spectrum
Absorption spectrum – shows the wavelengths of the
photons that are absorbed as gaps in a continuous
spectrum.
http://www.colorado.edu/physics/2000/quantumzone/in
dex.html
Uncertainty Principle
When doing quantum physics, we deal with
probabilities.
Examples: what is the probability that an
electron has so much velocity.
The probability that the electron is a certain
distance from the nucleus.
For certain pairs of variables: one example is
position and velocity, the uncertainties for the
variables are related.
The product of the uncertainties is approximately
equal to h/m.
h = Planck’s Constant = 6.6x10-34 J s
( x)( v) =h/m
If the spread in one of the variables goes down ,
the spread in the other goes up.
If you know one variable exactly, the other
variable can be anything.
Potential Energy Curve
PE
total energy
classically
forbidden
region
Classically
allowed
region
classically
forbidden
region
position
Potential energy curve.
• Classical particles can’t go to regions where the
potential energy is more than the total energy.
• Quantum mechanics says otherwise. That there
is a probability that the particle can be in a
restricted region.
• When a particle passes through the classically
forbidden domain, it is said to have tunneled
through a barrier.
Example:
An electron, or other tiny particle, is allowed
to ‘tunnel’ through a barrier via quantum
mechanics. There is a probability the particle
can pass through a wall.
People are made up of the same tiny particles.
However, the probability that a person can
pass through a wall, practically nonexistent.
Here we can see that quantum mechanics shows
that there is a probability that a particle can be
where classical physics says it’s forbidden.
Setting up a barrier we can see quantum tunneling.
go to tab 1 – 1.5
The graph represents the probability that the
particle is at that location.
http://www.quantum-physics.polytechnique.fr/
The height of the graph at each position is related
to the probability that the particle is located at
that position.
Wave behavior of particles
Earlier we mentioned how particles can be
described as waves.
Here is some evidence that particles behave
like waves.
By passing particles through a single slit, we
can observe a diffraction pattern. Diffraction
is how waves behave when they bend around
corners and spread out through gaps.
Double slit experiment shows that two
sources of particles (for example photons)
interfere with each other. Interference is a
wave property.
http://phys.educ.ksu.edu/vqm/index.html
Use single and double slit simulators to see
wave nature of particles.