Lecture VI: Line Spectra
and Quantum Mechanics
"A new scientific truth does not triumph by convincing its opponents and making them see the light but rather because its opponents eventually die, and a new generation grows up that is familiar with it."
"Atoms are not things"
"The 'paradox' is only a conflict between reality and your feeling of what reality 'ought to be'"
By the beginning of this century, cracks had appeared in the foundations of physics. Some things just weren't working.
In particular attempts to understand matter and energy on the atomic level using Newtonian mechanics were failing
In a kind of desperation, physicists began looking at a new "non-mechanical" description of atoms and light.
From this came Quantum Mechanics (QM) - the most powerful theory ever devised by humans.
There is only one problem - It doesn't make "sense".
of QM for astronomy were profound. It gave astronomers the key tools which
allowed them to decode light and use it to tell the stories of stars and
"One ought to be ashamed to make use of the wonders of science embodied in a radio set while appreciating them as little as a cow botanical marvels in the plant she munches"
Emission and Absorption Spectra
(Why do many interstellar gas clouds, "Nebula", Look red)
Last week we learned about blackbody radiation. A blackbody produces a "continuous" distribution of light - a continuous spectral energy distribution (SED).
But if you look at light from the sun
with a prism you see a rainbow of colors with dark lines superimposed on it.
Visible Spectrum Of The Sun - This visible spectrum of the Sun shows hundreds of dark absorption lines superimposed on a bright continuous spectrum. Here, the scale extends from long wavelengths (red) at the upper left to short wavelengths (blue) at the lower right.
If you look at light from an
interstellar gas cloud you only see a sequence of bright lines.
Visible Spectrum Of M17 - The visible spectrum of the hot gases in a nearby star-forming region known as the Omega nebula (M17). Shining by the light of several very hot stars, the nebula produces a complex spectrum of bright and dark lines (bottom), also shown here as an intensity trace from red to blue (center).
These are emission and absorption lines.
To really understand them you need quantum mechanics.
First lets look at something called Kirchoffs laws which were the first step in understanding "line spectra"
"hot" opaque body emits a continuous
Example -light bulb.
"hot" rarefied gas will emit a sequence of bright lines. These are
called emission lines.
Example - a neon sign.
3) A "cold" rarefied gas
placed in front of a hot opaque body will produce a continuous spectrum with
dark lines on top. These are called absorption lines.
Example - light from the sun.
Kirchoff's Laws Of Spectroscopy - A source of continuous radiation, here represented by a light bulb, is used to illustrate Kirchhoff's laws of spectroscopy. (a) The unimpeded beam shows the familiar continuous spectrum of colors. (b) When viewed through a cloud of hydrogen gas, a series of dark hydrogen absorption lines appears in the continuous spectrum. These lines are formed when the gas absorbs some of the bulb's radiation and re-emits it in random directions. Since most of the re-emitted radiation does not go through the slit, the effect is to remove the absorbed radiation from the light that reaches the screen at left. (c) When the gas is viewed from the side, a fainter hydrogen emission spectrum is seen, consisting of re-emitted radiation. The absorption lines in (b) and the emission lines in (c) thus have the same wavelengths. (If the gas were heated to incandescence, it would produce stronger emission lines at the same wavelengths.)
Every element (Hydrogen, Oxygen,
Nitrogen etc.) produces its own
set of emission and absorption lines.
They are the fingerprint of the elements.
Emission Spectrum Of Sample Elements - The emission spectra of some well-known elements.
The Origin of Lines
To understand line spectra you need a "model" of an atom.
By the turn of the century people were working with the idea that atoms were composed of negatively charged (-) electrons orbiting positively charged (+) protons the way planets orbit the sun.
(Neutrons which have no charge were discovered later)
Protons + Neutrons = the Nucleus
The electron and the proton have opposite charges and are always attracting each other via their electric fields.
Lets think about hydrogen the simplest and most abundant
atom in the universe with one electron and one proton.
The idea people wanted to work with was that atoms emitted and absorbed light by having the electron move closer or farther away from the nucleus.
Imagine a glass on a shelf - if it falls and hits the ground it breaks. Where did the energy come from to break it? From the gravitational field.
Imagine lifting a heavy air conditioner on to the shelf - Why is it so hard? Because you have to give up your energy to do work against the gravitational field.
These ideas relate to the concept of ENERGY which we will cover later. For now these intuitive "pictures" should help.
How does this relate to line spectra? People had the following picture in mind:
Emission - an electron falls a large distance away from the nucleus to smaller one and gives up energy in the form of light.
Absorption - an electron absorbs some light and gets moved out
to a larger distance.
Fine, but there is a Problem.
The classical theory of Light as "electromagnetic waves" says that lightwaves are emitted whenever a charge is accelerated.
Electrons in an orbit are always
accelerating just like planets around the sun.
Why don't they emit light all the time and spiral into the nucleus?
Absorption lines presented physicists with a huge problem.
The answer to the puzzle came with two "inventions".
The first was from Einstein who said that light, which was known to behave like a wave, could act like a particle as well.
Light particle = photon
The particle aspect of light was its ability to come in little discrete packages (quanta).
Atoms can absorb light the way you would
catch a baseball - all at once.
How can light be both a particle and a wave?
"Go away kid ya
"one can't believe impossible things"
The energy of a photon is related to its
frequency (and hence wavelength). Here is the important formula.
The next step came from Niels Bohr,
a Danish physicist who threw caution to the wind and
THERE ONLY CERTAIN DISCRETE ORBITS ALLOWED IN AN ATOM AND NO OTHERS.
Emission and Absorption Lines come from Electrons making JUMPS between these orbits.
In Bohr's model the nucleus is surrounded by shells of "possible" orbits. The electron can ONLY be in one of the orbits.
There is a "ground state" orbit. The electron can get no closer to the nucleus than this.
Higher orbits are called "excited states". An electron in an atom can get knocked into an excited state by getting hit by another atom.
Each orbit has a specific energy = Eorbit
A photon can only be absorbed when an electron jumps from a lower orbit to a higher one (this is another way to get an electron into an excited state)
But this can only happen if the photon's
energy is equal to the difference in energy between electron's orbits. This is
what allows a jump to be made.
E photon = Eorbit2 - Eorbit1
A photon can only be emitted when an
electron jumps from a higher orbit to a lower one.
Thus only photons with certain energies
(wavelengths) can be absorbed or emitted by an atom.
With Bohr's idea the connection between atoms and light was made explicit.
Now by analyzing star light astronomers could not only tell what kind material was out there but also what condition the atoms where in.
You could determine the density and temperature of astrophysical gases from spectral lines.
You could tell why Nebula appear red. It's electrons jumping from the second excited state of Hydrogen to the first excited state
All together it was a huge achievement.
Once Bohr let the cat out of the bag other physicists picked up on the idea that it was OK to develop theories where there was no "picture" possible in your head.
What matters is that your theory predict what occurs in experiments.
"All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics...It has survived all tests and there is no reason to believe there is any flaw in it. We all know how to use it and how to apply it to problems; and so we all have to live with the fact that nobody can understand it"
What came next:
After it was realized that light could
act as either a wave or a particle french physicist
De Broglie proposed that matter could also act as
either a particle or a wave.
He was right! This was the birth of the Wave-Particle Duality
"There is one simplification at least. Electrons behave in the same way as photons; they are both screwy, but in exactly the same way"
Weirdness #1: The Wave-Particle Duality
Waves and particles are about as different in physics as YES and NO are in logic.
Lets review some important wave properties.
Waves can interfere with each other.
If you have 2 waves and you
"superimpose" them. They can either cancel each other out or build on
each other (Constructive or Destructive Interference).
Wave Interference - Interference of two identical waves: (a) constructive and (b) destructive. In constructive interference, the two waves reinforce each other to produce a larger-amplitude wave. However, in destructive interference, the two waves exactly cancel out.
Particles don't do this!
You can see this phenomena if you pass
waves through a "double slit" experiment.
In the 1920's experiments show that you can shoot a beam of atoms at a double slit apparatus and it will also produce an interference pattern.
Even if you only let one atom go at a
time the interference pattern will slowly emerge.
So what is an electron? Is it a wave or a particle?
It depends what kind of question you ask. If you do a particle experiment you get particle results. If you do a wave experiment you get wave results.
So what do you have? A Wavicle?
There is no picture in your head for what an electron is!
Weirdness #2: The Heisenberg Uncertainty Principle
A single electron is described as a
Electron Wave in Bohr Orbit
Because the electrons can be described as a wave there is a basic relation that limits what can be known about their properties.
If x is the position of an electron and
p is it's momentum (related to Velocity) then
Heisenberg's Uncertainty Principle states
Where h is "plancks
constant" (h is very very small). The
"deltas" mean spread in the values of x or p. This equation says that
the uncertainty in both the electron's position and momentum has to be bigger
than the number .5h.
You can NEVER no these two quantities exactly.
This is not a problem with our equipment!
The fact that matter can act "wavey" sets fundamental limits on what we can know
about the world.
Compare Newton vs QM
QM: On a fundamental level the world is fuzzy!
1) Particles have no fixed identify.
They are indistinguishable.
"We have sought firm ground and found none. The deeper we penetrate, the more restless becomes the universe; all is rushing about and vibrating in a wild dance."
2) QM Tunneling - a particle trapped in
a box can "pop" out.
Very Strange Idea: Vacuum Genesis
The Universe Came out of "Nothing" because Nothing can not precisely exist!
"Anyone who has not been shocked by quantum mechanics has not understood it"
Weirdness #3: The Wavefunction
What are the waves in QM?
They are waves of probability!?!
In QM every physical situation can be described as a superposition of quantum waves.
To describe this physicists have what they call the Wave function.
Imagine a box with two compartments with a wall in between.
Now put an electron in it.
Which half of the box is the electron
According to the standard way of looking at things before a measurement is made the electron is in BOTH sides of the box at the SAME time!
When a measurement is made the wave function is said to COLLAPSE
W = S1
W = S2
What is a measurement?
An intrusion of consciousness into Physics?
The Observer Effects the Observed?
"If we take QM seriously as a picture of what's really going on then each measurement does more than just disturb: it profoundly reshapes the very fabric of reality"
The Parable of Schrodinger's Cat
Take a cat and put it in a box with a
jar of poison gas connected to a Geiger counter and a sample of radioactive
uranium. Now close the box.
The decay of uranium is a QM process. It is probabilistic and is described by a wave function.
If a radioactive decay is registered a hammer is tripped and the poison is released -> dead cat.
Before you look
the cat is both dead and alive! It is in a superposition
of deadness and aliveness states.
How can we get out of this paradox?
What if each piece of the wave function represents a separate possible UNIVERSE.
When an observation is made the wave
function doesn't collapse.
The Universe splits off into different branches!
In general a wave function will have not 2 but an infinite number of components.
W = a1S1 + a2S2 + a3S3 + ...
means there are an infinite number of Universes split off from each other!
This is a very weird idea!
Still, it is used in some aspects of cosmology where scientists want to talk about a collection or "ensemble" of Universes.
The Question here is why does our Universe look they way it does?
The answer is because it's the one that
can! There are many others that don't!
Quantum Mechanics and Mysticism
"We must continue to insist on the centuries long tradition of science in which we exclude all mysticism and insist on the rule of reason. Let no one use... a quantum experiment to claim faster than light communication or postulate any "quantum interconnectedness" between separate consciousness. Both are baseless. Both are mysticism. Both are moonshine."
The weirdness of QM has produced a lot of attention from the "New Age" movement.
The apparent connection between consciousness and physics has given some people the apparent license to say:
"Everything is connected to everything else in, like, everyway Man"
Beware of this. QM may be weird but it
is still based on empirical studies. It is Nature which sets the rules not us!
Policing the Boundaries of Science
Quantum Mechanics and Society
Of course none of this happens in a vacuum. At the same time that QM was being formulated the whole culture was being shaken up.
The Two World Wars trashed many of the
elements of faith that the older generation had come to trust. The younger generation were ready to toss off that faith.
Waiting for Godot, Samuel Beckett
ESTRAGON: I can't go on like this.
ESTRAGON: If we parted? That might be better for us.
ESTRAGON: And if he comes?
ESTRAGON: Well? Shall we go?
ESTRAGON: You want me to pull off my trousers?
ESTRAGON: (realizing his trousers are down) True.
He pulls up his trousers.
ESTRAGON: Yes, let's go.
They don't move.