![]() But what are t and t 1/2? Well, t is simply the amount of time that has passed since we counted the N initial atoms we began with, and t 1/2 is the half-life for the decay of those atoms. In other words, if we start with a population of atoms-or, as we’ll see in a moment, anything else that decays exponentially-that we’ll call N initial (that’s the initial number of those atoms), and we then multiply it by 1/2 raised to the power t/ t 1/2, then we can calculate the number of atoms we end up with. This type of decay-in which an average of half the members of a population disappear in a half-life of time … and then another half disappear in the next half-life … and then half of whatever is remaining disappear in the next half-life … and so on forever-is known as exponential decay. We can represent this type of decay in terms of a fairly simple formula: So if there are 1 billion atoms to start with, there will on average be 500 million atoms left after a time equal to their half-life. In other words, in a big group of the same type of radioactive atoms, there is a certain amount of time-called the half-life-that will pass before more-or-less half of the atoms will have decayed. after two half-lives 1 2 1 2 1 4 after one half-life of sample 1 2 fraction of sample remaining final mass of sample initial mass of sample 25.0 g 100. But even if we don’t know when any one particular atom will decay, we do know the overall average rate at which atoms in the pile will decay. What is the half-life of this radioactive isotope half-life of carbon-14 5730 y number of years half-life 11 460 y 2 half-lives 5730 y half-life Two half-lives have passed. ![]() The spontaneous nature of this decay means that it’s impossible to predict exactly when any individual atom in a huge pile of atoms will decay. (The fraction mf / mi is of course equivalent to the fraction or percentage of. mi the initial or original mass of undecayed sample. ![]() mf the final or remaining mass of undecayed sample. … it’s impossible to predict exactly when any individual atom in a huge pile of atoms will decay. Method 1: One way to solve for half-life is to use the following equation: t1/2 (t ln 1/2)/ (ln mf/mi) where: t1/2 half-life. A bit more precisely, some unstable isotopes of certain atoms (meaning certain versions of certain atoms that have certain, shall we say, non-standard numbers of neutrons in their nuclei) will spontaneously turn into different elements and in so doing release other particles and light along the way. Some types of atoms do a really weird thing-they spontaneously decay into other types of atoms. ![]()
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