image of the structure within the atom

  1. So for we have learned a bit about energy, including some of the different Units used to describe energy. Listed below are some units and ways to remember them….the letter or letters in parentheses are the abbreviations for these energy units.
  2. The Joule (J): 1 joule is the energy required to lift a one kilogram object 10 cm (i.e. your physics book). Also the Kinetic Energy of a 10 gram (.01 kg) marble moving at a speed of 10 m/s.
  3. The kilowatt-hour (kWh): 1 kilowatt hour is the amount of energy you use when using a one hundred watt bulb for 10 hours (or a 1 kilowatt-heater for one hour). Since a kilowatt is 1000 Watts = 1000 Joules/s, and an hour has 3,600 seconds, then 1kw-hr = 3,600,000 joules. And remember you don't pay much for a kilowatt-hour!
  4. The Calorie (or Kilocalorie). This is your basic food calorie. Actually, one calorie, with a small "c" is the amount of heat that must be absorbed by one gram of water before its temperature rises by 1o Celsius. In fact, this amount of heat absorbed per degree rise in temperature is known as the "heat capacity" of a substance. Since water is so common, its heat capacity is used as the definition for the calorie. A food Calorie (with a big "C"), or kilocalorie, is the amount of heat that must be absorbed by one kilogram of water before its temperature rises by 1o Celsius. A kilocalorie is equivalent to 4,186 joules. Since Calories and Joules are both forms of energy, they can be used interchangeably. For example, food in France is labeled with "Energy" instead of Calories…a cookie in for example contains about 1.2 MJ of Energy (1.2 Million Joules).
  5. Here's a new one: the Electron-Volt (eV): One electron volt is the kinetic energy gained by an electron when it is accelerated across a potential difference of one volt. To understand this another way, recall that: Potential Energy is equal to:

Electric potential x charge

P.E. = q x V

Thus one electron-volt equals (1.6 x 10-19 Coulombs) x (1.0 Joule/Coulomb) = 1.6 x 10-19 Joules. Of course, this is a tiny number compared to the energy of Moving Marbles, and baseballs. However, its generally not very useful to compare the energy of fundamental particles with the energy of visible objects. Still, an electron volt is a lot of energy for an electron (Since an electron has a tiny mass (9.1 x 10-31 kg)). In fact, using the relation that Kinetic energy equals 1/2 mv2 you can calculate that the speed of an electron with one electron-volt is moving about 600 kilometers/second! Another way to think of the electron volt is in terms of the "binding energy" of an electron to an atom. If a hydrogen atoms absorbs 13.6 electron volts of energy (or more) from a collision with another atom, or particle, then its single electron will be ejected, creating a hydrogen ion.

Mass, and Mass-Energy

Lets explore the relationships between mass and energy, and gain some practice using the units above. To start off … If we are dealing with baseballs and puppy dogs, then the best units to use are Joules (or MegaJoules). If we are talking about electrons or protons, however, the best units are electron volts, kilo-electron volts (keV), Mega-Electron Volts (MeV), or even Giga-Electron Volts (GeV). The mass energy of an electron, for example is 511 keV or .511MeV, a proton is 938Mev, ( or .938 GeV).

Since Mass Energy is calculated by using the relationship E = mc2, it is also possible to describe mass in terms of energy units: m = E/c2. Strange as it sounds, this is rather common. In particle physics, for example, the mass of the electron is described as: m = 511KeV/c2. As you might guess, it is also common to forget to mention the c2…you may read an article where a new particle is discovered "with a mass of 450 MeV." Of course, the real mass is 450 MeV/c2.

If you wish, click on this link for the "particle Adventure" to view a chart of fundamental particles, and see how their masses are described in the energy units used here…

This brings up an interesting point about the relationship between mass and energy: You might recall gamma (g) used in figured out how much time passes for different observers? Well, our friend gamma is also used in determining how much mass and energy a particle might have. Basically, the mass of a particle increases as a particle moves according to the relation: m = gmo, where mo is the "rest mass" of the particle. This means that if the particle is moving fast enough so that gamma equals 10, then you would measure its mass to be ten times greater than when the particle was at rest. Likewise, since E = mc2, you would measure its energy to be ten times greater than when it was at rest.

At Stanford Linear Accelerator Center, for example, Electrons are accelerated to velocities extremely close to the speed of light (v = .9999996c or greater!). Gamma at this speed is about 100,000! Thus the energies of electron produced are up to 100,000 times its rest energy. If you multiply the rest mass of 511keV by 100,000 you get about 50 GeV. Now this is a tremendous amount of energy for an electron, but remember an electron volt is a tiny unit of energy, so that this is only about 10-8 Joules, or about the Kinetic Energy of a Mosquito…

At other Accelerators, such as CERN in Switzerland, and Fermilab in Illinois, Protons, or atomic nuclei are accelerated rather than electrons. Since Protons are much more massive (approximately 2000 times the electron mass), they can have energies as high as 1 or 2 TeV (Trillion Electron Volts) at present. This is about 10-7 Joules, or about the Kinetic Energy of a fly…….Not impressed? Well, mankind has yet to produce accelerators of the type that nature has made routinely since the beginning of time. To date, the highest energy cosmic ray (probably a proton) that struck our atmosphere had approximately 50 Joules of energy.

That is about the energy of a well thrown baseball…but remember, the particle was a single proton and a baseball has bout 1025 protons within it. See the "Oh-My -God-Particle" website. Astronomers are in the process of identifying various types of cosmic particle accelerators. One such accelerator is shown here in an image recently taken by the Chandra x-ray telescope of the Crab supernova remnant. Note that this image itself shown below was complied by capturing X-ray photons coming from charged particles and atomic nuclei…essentially particles of light with energies greater than 1keV.

image of xray of relative energy

Is Energy Relative?

When electrons are accelerated across potential differences of 60 kilo-volts or so, their speeds become greater than half the speed of light. At this point, the simple formula: Kinetic energy = 1/2mv2 doesn't apply anymore. Instead an equation from special relativity: K.E. = Total Energy - Rest mass energy = gmoc2 - moc2 = moc2 (g -1) must be used. This is a lot easier than it looks. Consider a proton moving so fast that gamma equals eleven. Then g -1 = 10, and since moc2 = .938 GeV for a proton, the kinetic Energy is: 10 x .938 GeV = 9.38 GeV (billion electron volts).

At this point, you may thinking: why both doing this at all? After all, …achieving high gamma values requires considerable investments in time and money.

….Well, the idea is simply to produce a lot of energy is a small region of space and observe what happens. If you smash two particles together with 10 GeV each, then the resulting collision can liberate up to 20 GeV of energy (you can get 20GeV in this case only if one particle is the "anti-particle" of the other.) From that liberated energy, new particles, with various and unique rest masses are produced.

If the rest mass of a particle equals the energy released in a collision, then a particle will be born …. and discovered if it has never been seen before…the basic idea is to see what are the building blocks of matter (note that most of the particles "discovered in this manner are actually being searched for…they were often predicted earlier…often by applying conservation laws to earlier collisions).

Before we study matter on a "fundamental level" lets return to the relatively large domain of molecules and atoms. Along the way we will learn something about Temperature, Heat, Internal Energy, and Heat Transfer.

Zooming in and stopping…

If you print out this document on a dot matrix printer, each letter is made of hundreds, if not thousands of tiny dots of ink. The better the printer, the smaller the dots. If you look with a microscope on low power at any letter, you will certainly see all the dots. Likewise, all matter is made of smaller constituents called molecules, and even smaller constituents called atoms. Presumably this is nothing new, but you may be wondering how to prove this without looking through a "Scanning Tunneling Electron Microscope" which will reveal the existence of individual atoms.

Ever since Democratus of Abdura in Ancient Greece proposed that all things are made of atoms, people have been looking for proof. It was none other than Albert Einstein who proposed the first proof (remember the miracle year!) by watching the random motion of a dust particle suspended in a flask of hot water as it was buffeted by the motions of individual water molecules. Albert actually derived a formula for how far the dust particle would move in a given time due to the collisions with water Molecules, based on the temperature of the water, and the mass of the dust particle. When his (statistical) result was verified experimentally, the scientific community had the proof of an idea that was already part of the scientific "paradigm"…at least the issue was settled!

image of water oxygen atom rotating around a hydrogen atom

As you know, Water Molecules, like all molecules, are atoms held together by the electric force. If you put an Oxygen atom near a Hydrogen atom, the outer electrons in the Oxygen atom will feel a small extra pull towards the Hydrogen atom and are more likely to be found on that side of the atom. The Electron from the Hydrogen atom, on the other hand will be repelled by these rude Oxygen electrons and is likely to be found on the opposite side of the Hydrogen atom (from the Oxygen atom).

This charge separation is called an "Electric Dipole" It also means that the positive and negative charges attract more than negative charges repel other negative charges, and the positive charges repel other positive charges because the separation for unlike charges is closer than it is for like charges. See the Electric Dipole applet from the physics 2000 Web site

 

You may also be aware that the Electric force is so much stronger than the gravitational force that we can ignore the effects of gravity in trying to understand how atoms are bound together. The only reason we are aware of gravity at all is because it is only attractive…the entire Earth's Mass is pulling on us..if there were positive and negative gravitational charges in nearly equal numbers, then Gravity would be something you'd need very expensive equipment to study!

As it is, you can easily experiment with Electric and Gravitational forces. Place your hand on the tabletop. Why does it rest there rather than falling right through (in response to gravity)? You might answer: because the tabletop is solid. On the other hand (whoops)..the "solidity" of the table is simply due to the electrons in your hand repelling the electrons in the surface layer of the table.

These electrons never actually touch one another, but simply are pushed closer together until the electrical force is enough force is enough to balance out the gravitational force (remember, the strength of the electrical force varies as the inverse square of the distance). You never even make "particle to particle" contact with the table! With this in mind, what does it mean to touch something?

If the electrical charges could be "turned off" and you somehow didn't fall apart, then you hand would pass right through the table. Very few electrons would collide with one another, and even fewer nuclei would collide. We would all be "Ghosts in the Machine" without the strong electrical interactions.