First, your bus can't be going at the speed of light because massive objects are strictly forbidden from traveling at that speed. Even to being traveling near the speed of light would require a fantastic expenditure of energy.
But suppose that the bus were traveling at 99.999999% of the speed of light and you were to run toward its front at 0.000002% of the speed of light (about 13 mph or just under a 5 minute mile). Now what would happen?
First, the bus speed I quoted is in reference to some outside observer because the seated passengers on the bus can't determine its speed. After all, if the shades are pulled down on the bus and it's moving at a steady velocity, no one can tell that it's moving at all. So let's assume that the bus speed I gave is according to a stationary friend who is watching the bus zoom by from outside.
While you are running toward the front of the bus at 0.000002% of the speed of light, your speed is in reference to the other passengers in the bus, who see you moving forward. The big question is what does you stationary friend see? Actually, your friend sees you running toward the front of the bus, but determines that your personal speed is only barely over 99.999999%. The two speeds haven't added the way you'd expect. Even though you and the bus passengers determine that you are moving quickly toward the front of the bus, your stationary friend determines that you are moving just the tiniest bit faster than the bus. How can that be?
The answer lies in the details of special relativity, but here is a simple, albeit bizarre picture. Your stationary friend sees a deformed bus pass by. Ignoring some peculiar optical effects due to the fact that it takes time for light to travel from the bus to your friend's eyes so that your friend can see the bus, your friend sees a foreshortened bus—a bus that is smashed almost into a pancake as it travels by. While you are in that pancake, running toward the front of the bus, the front is so close to the rear that your speed within the bus is miniscule. Why the bus becomes so short is another issue of special relativity.
I'm afraid that you confuse the hypothetical with the actual. While people have hypothesized about superluminal particles called tachyons, they have never been observed and probably don't exist. This speculation is based on an interesting but apparently non-physical class of solutions to the relativistic equations of motion. Although tachyons make for fun science fiction stories, they don't seem to have a place in the real world.
Most modern nuclear weapons produce a super-critical mass of fissionable nuclear fuel by crushing a sphere of that material with high explosives. As the material's size shrinks, its density increases and it passes rapidly through critical mass to achieve a highly super-critical mass. Nuclear chain reactions then grow exponentially in the material and huge amounts of energy are released. However, the process of crushing a solid sphere of metal to several times its normal density requires sophisticated high explosives triggered at precisely the right moments. The triggering is done with very high-speed electronic devices and explosive detonators that respond almost instantly to high voltage pulses. Perhaps the most critical components in this system are high speed, high voltage switches known as krytron tubes. Because these devices have limited uses outside of nuclear weapons, their export is tightly controlled and it's a big news story whenever someone is caught trying to smuggle them outside the United States.
This questions asks how you can predict the amount of a fissionable nuclear fuel you must assemble in order for that fuel to experience self-sustaining nuclear fission chain reactions. A self-sustaining nuclear chain reaction can only occur when each fission within that material causes an average of one subsequent fission. The size, shape, and density of the nuclear fuel are important to the chain reaction because they determine how much opportunity fragments from one fission event will have at inducing subsequent events elsewhere within the fuel. A properly shaped piece of fuel that is just large enough and dense enough to experience a self-sustaining nuclear chain reaction is said to be at critical mass. Below the critical mass, the chain reaction won't be able to sustain itself and will gradually dwindle away. Above the critical mass, the chain reaction will grow stronger exponentially. Since crossing the threshold from below critical mass to above critical mass has dramatic consequences, it can be quite important to know the point at which it occurs.
The basic calculation of critical mass is straightforward in principle, but it requires a thorough understanding of the nuclear fuel. Because you need to know how likely one nuclear fission is to cause a subsequent nuclear fission, you must know both the types of fragments you can expect from the first nuclear fission and the likelihood that each fragment will induce a subsequent fission in another atomic nucleus before that it escapes from the nuclear fuel. Because the range of possible fragments, their kinetic energies, and their paths through the nuclear fuel are so vast, an accurate calculation of critical mass is extremely complicated. As an indication of the difficulty, note that fission fragments may bounce off nuclei without inducing fission, so that you must consider bent paths as well as straight ones. Not surprisingly, the calculation of critical mass is too difficult to do exactly, even with the help of computers. In fact, one of the reasons that Germany didn't develop nuclear weapons during World War II was that its scientists miscalculated the critical mass of a fission bomb based on enriched uranium and thought that they would need many tons of enriched uranium rather than the true critical mass of about 52 kilograms. Certain that a critical mass of enriched uranium was unattainable, they didn't pursue the project.
While both fission and fusion convert substantial fractions of the mass in a thermonuclear weapon into energy, most of the bomb's initial matter remains matter, not energy. When a uranium nucleus fissions to become smaller nuclei, about 0.1% of the uranium nucleus's mass becomes energy. When two deuterium nuclei—the heavy isotope of hydrogen—fuse together to become helium, about 0.3% of the deuterium nuclei's masses become energy. Despite these seemingly small percentages, this scale of matter to energy conversion dwarfs that of chemical explosives, which convert only parts per billion of their masses into energy.
While fusion is somewhat more energy efficient than fission, that's not the whole reason why hydrogen bombs (thermonuclear bombs) are more powerful than uranium bombs (fission bombs). The main reason is that thermonuclear bombs can be much larger than fission bombs because there is no upper limit to the amount of hydrogen you can assemble in a small region of space. In contrast, if you assemble too much fissile uranium in a small region of space, a chain reaction will begin and the material will overheat and explode. At the height of the cold war, the Soviet Union built gigantic thermonuclear weapons with explosive yields as large as 100 megatons of TNT.
There are so many non-medical uses for X-rays that I'll limit myself to two: industrial imaging and X-ray crystallography. Industrial X-ray imaging is used frequently in manufacturing to inspect finished materials. An important example of this imaging is in weld inspection. After a sheet of steel has been rolled into a pipe and the seam of that pipe has been welded closed, it's often important to inspect the weld to be sure that it's solid and leak free. Sometimes a weld that looks perfect to the eye has hollow spots or other flaws that can only be seen by looking through the material of the weld. This inspection is done with high energy X-rays—X-rays that are able to penetrate a thick steel plate to look for bubbles or unwanted inclusions.
X-ray crystallography is an important tool for materials science and molecular biology. Just as the colored interference patterns that appear on a soap bubble when sunlight reflects from that bubble tell you something about the structure of that soap bubble, so the X-rays that reflect from a crystal tell you something about the structure of that crystal. X-rays experience interference after they reflect from a crystal and the interference patterns can tell you where individual atoms are located within a crystal or within the molecules from which the crystal is made. Materials scientists use this information to understand the crystals they have produced while molecular biologists use it to understand the molecular structures of complicated biological molecules.
Subatomic particles and fundamental particles aren't necessarily the same—some subatomic particles are built from several fundamental particles. That's the case for two of the most important subatomic particles: the proton and the neutron. Each of these particles is built from three fundamental particles known as quarks. The proton contains two "up" quarks and one "down" quark. The neutron contains one "up" quark and two "down" quarks. However, another important subatomic particle is also a fundamental particle: the electron. Virtually all matter is composed of these three subatomic particles: protons, neutrons, and electrons.
The list of fundamental particles—particles that are not known to be composed of other particles—is relatively short. It includes 6 types of quarks, which are given the arbitrary names "up", "down", "charm", "strange", "top", and "bottom". These quarks are never found by themselves but are instead used to build two major classes of subatomic particles: baryons (including protons and neutrons) and mesons. The list of fundamental particles also includes 6 types of leptons, which are given the names "electron", "electron neutrino", "muon", "muon neutrino", "tau", and "tau neutrino". These leptons are found by themselves and aren't used to build any other subatomic particles. These quarks and leptons are described as fermions and each has an associated antiparticle.
In addition to quarks and leptons, there are a number of fundamental particles that allow the fundamental fermions to interact with one another. These interaction particles are described as bosons and include the "photon", "W+ Boson", "W- Boson", "Z Boson", 8 different "gluons", and a particle called "Higgs" (which has not yet been observed but is thought to exist).
The list of subatomic particles that can be formed from the fundamental particles is extremely long and listing it here wouldn't be very enlightening. The only subatomic particles that are common in nature are protons, neutrons, electrons, and photons. Some of the others appear through nuclear or subnuclear processes in radioactive materials, nuclear reactors, particle accelerators, or celestial objects, but most of these exotic subatomic particles haven't been common since moments after the big bang.
As Einstein's famous formula points out, mass and energy are equivalent in many respects. In most situations, mass is conserved and so is energy. But at the deepest level, it's actually the sum of those two quantities that's conserved. When matter and anti-matter collide, they often annihilate one another and their mass/energy is converted into other forms. For example, when an electron and an anti-electron (a positron) collide, they can annihilate to produce two or more photons of light. There is no fundamental law that prevents matter from being created or destroyed but there is a fundamental law that mass/energy must be conserved. In this case, the masses of the electron and positron become energy in the massless photons. Overall, mass/energy has been conserved but what was originally mass has become energy. The fact that when matter and anti-matter annihilate, the product is usually energy, makes this mixture attractive as a possible super-rocket fuel. But don't hold your breath; anti-matter is incredibly difficult to make or store.
You can measure the magnetic fields in which certain atoms reside with the help of nuclear magnetic resonance (NMR). This technique examines the magnetic environment of the atom's nucleus by determining how much energy it takes to change the orientation of the nucleus. Since the nucleus is itself magnetic, it tends to align with any magnetic field—like a compass. The stronger that magnetic field, the harder it is to flip the nucleus into the wrong direction.
Since radioactivity is a feature of atomic nuclei, the only way to alter radioactivity is to alter atomic nuclei. But there aren't many ways to change atomic nuclei. Of various atomic and subatomic particles, only a neutron can enter a nucleus easily and cause it to rearrange. However, it's more common for a neutron to increase radioactivity than to destroy it, so that's not a good approach. Furthermore, the only practical way to obtain neutrons is with radioactivity.
Heating a collection of nuclei can cause them to collide and rearrange. However, this process is also fraught with problems. The products of the fusion and fission events that occur when nuclei collide will probably be radioactive themselves, so that it's unlikely that heating radioactive materials will make them less radioactive. Instead, it's likely that heating radioactive materials will make them more radioactive. Furthermore, the temperatures at which nuclei will begin to collide are extraordinarily high. Even the smallest nuclei repel one another fiercely so that they need temperatures of 100 million degrees C or more to begin colliding effectively. Larger nuclei, such as those common in nuclear wastes, won't collide until their temperatures exceed 1 billion degrees C. The only way to reach these temperatures is with nuclear weapons and they certainly don't reduce the radioactivity of nearby materials. In short, the only way to get rid of radioactivity is by waiting patiently.
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