Soon after Becquerel's discovery, Marie Sklodowska Curie began studying radioactivity and completed much of the pioneering work on nuclear changes.
Curie found that radiation was proportional to the amount of radioactive element present, and she proposed that radiation was a property of atoms (as opposed to a chemical property of a compound).
But it's not as useful if we're trying to figure out how much of a compound we have after 1/2 of a half-life, or after one day, or 10 seconds, or 10 billion years.
And to address that issue in the last video, I proved that it involved a little bit of sophisticated math.
The element is said to "transmutate" into another element that is two z units smaller.
For example, you have 5.97 u Ci of P-32 now and you want to know how much was there 9 days ago.Again, we find a "chance" process being described by an exponential decay law.We can easily find an expression for the chance that a radioactive atom will "survive" (be an original element atom) to at least a time t.But if you're curious, that's where we proved the following formula.That at any given point of time, if you have some decaying atom, some element, it can be described as the amount of element you have at any period of time is equal to the amount you started off with, times e to some constant-- in the last video I use lambda. And then for a particular element with a particular half-life you can just solve for the k, and then apply it to your problem.for a parameter and constant (known as the decay constant), where is the exponential function and is the initial value.Exponential decay is common in physical processes such as radioactive decay, cooling in a draft (i.e., by forced convection), and so on. This is why it is such a big concern when a nuclear submarine sinks... (By the way, you are mostly Carbon-12, which is not radioactive.Eventually, the salt water will eat through the steel and release the Plutonium (which, as you know, is quite lethal.) They usually talk about either trying to raise the sub or encase it in concrete where it rests. That's why we are called "Carbon-based life forms." Man, I've really watched too much Star Trek.)Scientists use Carbon-14 to make a guess at how old some things are -- things that used to be alive like people, animals, wood and natural cloths. Anyway, they make an estimate of how much Carbon-14 would have been in the thing when it died...Exactly the same treatment can be applied to radioactive decay.However, now the "thin slice" is an interval of time, and the dependent variable is the number of radioactive atoms present, N(t). If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval.