You won’t need to calculate the natural logarithm of 2—remember, no calculators are
allowed on the test. What you will need to know is that, at time t = , one-half of a
given radioactive sample will have decayed. At time t = 2 , one-half of the remaining
half will have decayed, leaving only one-quarter of the original sample. You may
encounter a graph that looks something like this:
The graph of decay vs. time will get steadily closer to the x-axis, but will never actually
reach it. The fewer atoms that remain undecayed, the less activity there will be.
Nuclear Reactions
Nuclear reactions are effectively the same thing as radioactivity: new particles are formed
out of old particles, and the binding energy released in these transitions can be
determined by the equation E = mc^2. The difference is that nuclear reactions that are
artificially induced by humans take place very rapidly and involve huge releases of energy
in a very short time. There are two kinds of nuclear reaction with which you should be
familiar for SAT II Physics.
Nuclear Fission
Nuclear fission was used in the original atomic bomb, and is the kind of reaction
harnessed in nuclear power plants. To produce nuclear fission, neutrons are made to
bombard the nuclei of heavy elements—often uranium—and thus to split the heavy
nucleus in two, releasing energy in the process. In the fission reactions used in power
plants and atomic bombs, two or more neutrons are freed from the disintegrating
nucleus. The free neutrons then collide with other atomic nuclei, starting what is called a
chain reaction. By starting fission in just one atomic nucleus, it is possible to set off a
chain reaction that will cause the fission of millions of other atomic nuclei, producing
enough energy to power, or destroy, a city.
Nuclear Fusion
Nuclear fusion is ultimately the source of all energy on Earth: fusion reactions within
the sun are the source of all the heat that reaches the Earth. These reactions fuse two or