Radioactivity means that atoms decays. The reason for this decays is that they are instable. A atomic nucleus is instable when he is to heavy or when a balance is missing between the protons and the neutrons. Every atom which has got a higher number of nucleons (protons and neutrons togehter) than 210 is instable. There are three types of decays: alpha decay, beta decay and gamma decay. Because it is impossible today to say which atomic nucleus will be the next who decays there statistics. We can say how many atomic nucleus will decay in a certain time. This is the princip for half lifes. After one half life a half of the atomic nucleus of a certain material decayed. Plutonium-239 for example has got a half life 24,000 years, radium-228 has got a half life of 6.7 years, thorium-232 has got a half life of 14,000,000,000 years and polonium-212 has got a half life 0.0000003 seconds. There are many physical properties, but I will talk about the acivity now. The activity is the number of decays devided by a certain time. the unit of the activity is becquerel. 1 becquerel is one decay per second. So 20 becquerels are 20 decays per second. To prove these decays there is a geiger counter. It consists of a closed tube which is often filled with argon. At the end of the tube there is a wire, which is not allowed to touch the other end of the tube or the walls. The wire is charged positive and the walls are charged negative. A radioactive particle which flows into the tube ionizes one or a few gas atoms. The out-pushed electrons go to the wire. The consequence is a voltage surge. This voltage surge is shown on an output device as a decay. On the photo there shown a geiger counter.
For non-relativistic objects Newton defined momentum, given the symbol p, as the product of mass and velocity -- p = m v. When speed becomes relativistic, we have to modify this definition -- p = gamma (mv)
Notice that this equation tells you that for any particle with a non-zero mass, the momentum gets larger and larger as the speed gets closer to the speed of light. Such a particle would have infinite momentum if it could reach the speed of light. Since it would take an infinite amount of force (or a finite force acting over an infinite amount of time) to accelerate a particle to infinite momentum, we are forced to conclude that a massive particle always travels at speeds less than the speed of light.
Some text books will introduce the definition m0 for the mass of an object at rest, calling this the "rest mass" and define the quantity (M = gamma m0) as the mass of the moving object. This makes Newton's definition of momentum still true provided you choose the correct mass. In particle physics, when we talk about mass we always mean mass of an object at rest and we write it as m and keep the factor of gamma explicit in the equations.
Probably the most famous scientific equation of all time, first derived by Einstein is the relationship E = mc2.
This tells us the energy corresponding to a mass m at rest. What this means is that when mass disappears, for example in a nuclear fission process, this amount of energy must appear in some other form. It also tells us the total energy of a particle of mass m sitting at rest.
Einstein also showed that the correct relativistic expression for the energy of a particle of mass m with momentum p is E2 = m2c4 + p2c2. This is a key equation for any real particle, giving the relationship between its energy (E), momentum ( p), and its rest mass (m).
If we substitute the equation for p into the equation for E above, with a little algebra, we get E = gamma mc2, so energy is gamma times rest energy. (Notice again that if we call the quantity M =gamma m the mass of the particle then E = Mc2 applies for any particle, but remember, particle physicists don't do that.)
Let's do a calculation. The rest energy of an electron is 0.511 MeV. As we saw earlier, when an electron has gone about 10 feet along the SLAC linac, it has a speed of 0.99c and a gamma of 7.09. Therefore, using the equation E = gamma x the rest energy, we can see that the electron's energy after ten feet of travel is 7.09 x 0.511 MeV = 3.62 MeV. At the end of the linac, where gamma = 100,000, the energy of the electron is 100,000 x 0.511 MeV = 51.1 GeV.
The energy E is the total energy of a freely moving particle. We can define it to be the rest energy plus kinetic energy (E = KE + mc2) which then defines a relativistic form for kinetic energy. Just as the equation for momentum has to be altered, so does the low-speed equation for kinetic energy (KE = (1/2)mv2). Let's make a guess based on what we saw for momentum and energy and say that relativistically KE = gamma(1/2)mv2. A good guess, perhaps, but it's wrong.
Now here is an exercise for the interested reader. Calculate the quantity KE = E - mc2 for the case of v very much smaller than c, and show that it is the usual expression for kinetic energy (1/2 mv2) plus corrections that are proportional to (v/c)2 and higher powers of (v/c). The complicated result of this exercise points out why it is not useful to separate the energy of a relativistic particle into a sum of two terms, so when particle physicists say "the energy of a moving particle" they mean the total energy, not the kinetic energy.
Another interesting fact about the expression that relates E and p above (E2 = m2c4 + p2c2), is that it is also true for the case where a particle has no mass (m=0). In this case, the particle always travels at a speed c, the speed of light. You can regard this equation as a definition of momentum for such a mass-less particle. Photons have kinetic energy and momentum, but no mass!
In fact Einstein's relationship tells us more, it says Energy and mass are interchangeable. Or, better said, rest mass is just one form of energy. For a compound object, the mass of the composite is not just the sum of the masses of the constituents but the sum of their energies, including kinetic, potential, and mass energy. The equation E=mc2 shows how to convert between energy units and mass units. Even a small mass corresponds to a significant amount of energy.
In the case of an atomic explosion, mass energy is released as kinetic energy of the resulting material, which has slightly less mass than the original material.
In any particle decay process, some of the initial mass energy becomes kinetic energy of the products.
Even in chemical processes there are tiny changes in mass which correspond to the energy released or absorbed in a process. When chemists talk about conservation of mass, they mean that the sum of the masses of the atoms involved does not change. However, the masses of molecules are slightly smaller than the sum of the masses of the atoms they contain (which is why molecules do not just fall apart into atoms). If we look at the actual molecular masses, we find tiny mass changes do occur in any chemical reaction.
Please accept my apologies for a misunderstanding in the story... his uncle was NOT, I repeat, NOT injected with cow sperm, it was merely his glove... not as exciting, I know, but, hey, I think its a good thing!
Ever wonder how cows get pregnant? Well, sex, of course, works, but what about those really fat cows that can't move? That's what I wondered, so I asked everyone's favorite Farm Boy, Ross Mosher, who explained to me the process of artificially inseminating cows. First, the sperm is collected into a syringe. How this is achieved, I was not told, nor did I think to ask, but I'd have to assume through artifical cow masturbation. Next, an extremely long rubber glove is placed on the arm of the farmer. This glove reaches up to his shoulder. The farmer then sticks his arm up the back of the cow, until he can feel her uterus. Next, the syringe (with an extra long, fine needle) is placed parallel to the arm inside the cow, and slid in along the arm. The sperm is injected, and the cow becomes inpregnated. He then told me a horror story of how his uncle accidentally got the needle in his glove... and he didn't realize it, and was injected with cow sperm... At SLAC, and in any particle physics facility, we also see the reverse effect -- energy producing new matter. In the presence of charged particles a photon (which only has kinetic energy) can change into a massive particle and its matching massive antiparticle. The extra charged particle has to be there to absorb a little energy and more momentum, otherwise such a process could not conserve both energy and momentum. This process is one more confirmation of Einstein's special theory of relativity. It also is the process by which antimatter (for example the positrons accelerated at SLAC) is produced.
Newton's laws of motion give us a complete description of the behavior moving objects at low speeds. The laws are different at speeds reached by the particles at SLAC.
Einstein's Special Theory of Relativity describes the motion of particles moving at close to the speed of light. In fact, it gives the correct laws of motion for any particle. This doesn't mean Newton was wrong, his equations are contained within the relativistic equations. Newton's "laws" provide a very good approximate form, valid when v is much less than c. For particles moving at slow speeds (very much less than the speed of light), the differences between Einstein's laws of motion and those derived by Newton are tiny. That's why relativity doesn't play a large role in everyday life. Einstein's theory supercedes Newton's, but Newton's theory provides a very good approximation for objects moving at everyday speeds.
Einstein's theory is now very well established as the correct description of motion of relativistic objects, that is those traveling at a significant fraction of the speed of light.
Because most of us have little experience with objects moving at speeds near the speed of light, Einstein's predictions may seem strange. However, many years of high energy physics experiments have thoroughly tested Einstein's theory and shown that it fits all results to date.
