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Photon-Electron Interactions
Mass-Mass Interactions
Gravitation and Gravity
Molecular Velocity and Temperature
CHAPTER 1 Introduction

Classical Physics Vs. Quantum Physics


If you have a bad day and need to go to a physics text book for some deep relaxation, you will find some interesting things. To oversimplify, these books are, for the most part, still classical physics texts. If you look up concepts light or electromagnetic radiation, you won't find a clear, simple definition. You will find a definition that has a form like: "Light is something that has this kind of behavior." If you look up the words energy or heat you will find the same thing. Heat is that which moves from a place of high temperature to a place of low temperature. Energy is the ability to do work. It is all very unsatisfactory as explanations go. It is not such an easy study. You have to get into quantum mechanics to get real satisfaction.

If you go about the business of reading about quantum physics, the power to explain the world around us is much better but, like in Olympic diving, the degree of difficulty is out of sight. Classical physics is macroscopic physics, no peaking inside atoms or molecules to explain the world. Macroscopic physics does a good job and poses no problem except when you need to explain actions at a distance, i.e. gravity and light.

Most of what we do in atmospheric sciences--the kind of mathematical reasoning we use--is based on classical physics and most of what we knew around 1900 does rather well today, but that doesn't always mean the explanations are crystal clear rather than clear as mud. Some quantum physics, post-classical physics, really helps explain things. We will use it when it helps us but without the arcane math. We won't need it much for gravity because we always assume it to be constant so it won't mess up our equations. We will need quantum ideas for the study of radiation. We will need some quantum physics to help us understand concepts like temperature and heat and perhaps even molecular motions and the behavior of gases. It might even help us understand what pressure is. Hope springs eternal.

Photon-Electron Interactions

If you were to take a bunch of light and divide it and subdivide it until you couldn't do it anymore and had the smallest possible bunch of light, well, that fundamental unit of light is called a photon. It is a fundamental subatomic particle like an electron. Photons can bounce back and forth 1) between charged particles, 2) within an atom, or 3) be emitted from an atom and travel across the vastness of space. The photon has no mass when it is at rest but travels at 300,000 m/sec, the speed of light. But the photon is not at rest and so it has momentum. Photons are exchanged between electrons.

If you were to take a bunch of gravity and divide it and subdivide it until you couldn't do it anymore and had the smallest bunch of gravity possible, that is called a graviton. It is a fundamental subatomic particle like a photon. Gravitons are exchanged between particles with mass. We won't bother much with gravitons in our discussions but it is neat to better understand gravity. In our study of the atmosphere we will hold gravity to be constant (9.8 meters per second per second).

Electrons repel each other! Why? As two electrons approach each other they exchange photons. When the photon hits an electron, the momentum of the photon causes the electron to rebound away. The closer together the electrons are the more likely the exchange of photons (Like two gunfighters at a high-noon shoot-out.) will take place and they are to be repelled. The repulsion of electrons gets stronger the closer they get to each other. So what happens to things without charge when they get close together? That gets us back to gravitron again. All things with mass attract each other by sharing gravitrons. The closer they get together the more likely they will share gravitrons and the greater will be the attraction. If things have both electrons with photons to repel with and mass with gravitrons to attraction with, attraction and repulsion will happen at the same time.

Max Planck got us off to thinking about photons of light. He concluded that not all photons were alike. They differed in their amount of energy and in their oscillatory behavior, they had very specific wavelengths for the energy they contained. He wrote a formula that tied it all together ( Eq. 1).

(EQ 1)

where E = energy, n = an integer number, h is Planck's constant (6.6 x 10-34 Joule sec-1), and n is the frequency of the light (the photon). It might be useful, here, to rewrite equation ( Eq. 1) as follows:

(EQ 2)

Eequation ( Eq. 2) tells us that the ratio of the energy of the photon to Plank's constant times the frequency must be an integer. There is a ratio for n=1, for n=2, for n=3, etc. You specify the frequency of light (or its photons) and it can have one and only one level of energy. A photon of blue light with a wavelength of 0.5000 m has a fixed amount of energy. Once you accept the quantized nature of photons then you are permitted to drop the n and just write E = hn. A photon then is hn and E is its energy.

Niels Bohr, the famous Dane, studied the orbits of electrons around the nucleus of an atom and found the following relationship

(EQ 3)

where m = mass of the electron, v = the velocity of the electron in its orbit, r = the radius of the orbit, n is an integer number, and h = Planck's constant. We can rewrite ( Eq. 3) as

(EQ 4)

In Eq. 4 mvr is the angular momentum. This all means that the angular momentum of electrons in their orbits is "quantized" like photons. For a given nucleus only certain orbits are possible, one for each integer n. Planck's and Bohr's notions are at the heart of quantum physics. Some things come in packages of fixed size and none other! This new physics of photons, electron, and electron orbits is Quantum ElectroDynamics: QED.

The three principals of QED:

One of the things that physicists like do is to build TOEs. TOE = theory of everything. The classical physicists did their best to unite the branches physics to a singular common physics. For example they tried to unite mechanics and thermodynamics into one science. They wanted to be able to derive the laws of thermodynamics from mechanics. They were not able to do it. The quantum physicists seem to have everything in their current TOE except gravity. Hawkings and others say "string theory" and "superstring theory" will finally unite all of physics. A string is something smaller than electrons, and other sub-atomic particles. They are 10-34 m in size (see the size of Planck's constant!). We will see if string theory wins the day and a new, new metaphysics is written. Don't expect books on the weather to change much. Again we can largely resist the temptations to get all the way to TOE. We can focus on the junction of classical and quantum physics and study photons and the things the photon do.

So what happens when a photon is absorbed by an electron? The orbit of the electron is changed in some way when a photon is absorbed. If the photon absorbed does not have just the right amount of energy (quantum) to cause one of the possible orbital changes, then the photon "bounces" away as a scattered or reflected light. Scattering and reflection are very important in atmospheric processes. Absorption is important as well. What happens to the momentum of the photon? It causes the electron to be pushed in a direction and perhaps faster than before. Or, the absorbed photon could cause the molecule to rotate or spin a bit differently, again it takes a specific amount of photon energy to cause one of the many possible new (quantized) spins. Or, it could cause the atoms of the molecules to vibrate the bonds between two atoms differently. Such vibrations are quantum (fixed amounts), i.e. the need a certain kind of photon with just the right amount of energy. In any case, when the momentum is given over to increased energy within the molecule, the molecule has more energy, higher molecular velocity, and its temperature goes up. It has more heat. It is hotter. Giving off photons is the reverse sort of quantum processes. When we begin to talk about radiation and the atmosphere we will return to these quantum ideas. At that point we are going to need to understand the quanta of electromagnetic radiation, i.e. photons.

Mass-Mass Interactions

Gravitation and Gravity


Masses attract each other. This attraction, perhaps due to the sharing of gravitrons, is proportional to the magnitude of the masses and inversely proportional to the distance between the centers of the mass. The more mass the more gravitrons. The closer together the more sharing can go on.

(EQ 5)

In Eq. 5 G* is the constant of proportionality known as Newton's Universal Gravitational Constant ( Eq. 6).

(EQ 6)

G is gravitation. Because the Earth spins there is another acceleration (the centripetal acceleration) in the up and down direction that we must add to the gravitation attraction and we call the sum of the two accelerations gravity. These accelerations are, like all accelerations, vectors. The have both magnitude and direction. Adding two accelerations that do not point in exactly the same directions must be added by vector addition. See the chapter on atmospheric dynamics if you need to look into this concept right now.

Molecular Velocity and Temperature


All molecules in the atmosphere are in motion. The have velocities. They move around, mix together and have collisions with each other. The consequences of these interactions depend on how close the molecules are to each other, what their velocities are, and what kind of molecules they are.

If you were to go out and take a sample of air and if your were to measure the velocities of each of the molecules you sampled, you would find a spectrum of velocities present.They do not all have the same velocity. The frequency (number counted) of each velocity is graphed in Figure 9.

FIGURE 9 Spectrum of Molecular Velocities

Molecular velocity depend on what kind of a substance is involved (the constant R) and on the temperature of the substance.

(EQ 7)

It is useful to solve ( Eq. 7) for temperature at this point as it will give us a nice definition of temperature.

(EQ 8)

(EQ 9)

The temperature of a gas is related to the molecular velocity squared ( Eq. 9). If you add energy to a gas (heat it) molecular velocities increase and temperature rises. It is important to realized the difference between heat and temperature.


The Atmosphere - 22 SEP 95
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