What is a radioactive element's half-life?

Answer 1

The time it takes for a half of the element to decay. In Example: Technetium-99 has a half life of 6 hours. If you begin with a sample of 100g, then after 6 hours you will have 50 grams, at 12 hours you will have 25 grams and so on; however it will NEVER reach 0 (it will remain in exponentially small ammounts because of the asymptote in the graph). This specific exponential decay is shown by the equation y=100(0.5)((1/6)x)

Answer 2

First, it isn't very accurate to talk about a radioactive "element"; you should talk about radioactive isotopes. Different isotopes of the same element can have very different behavior in this sense. For example, hydrogen-1 and hydrogen-2 are stable, while hydrogen-3 is not (half-life about 19 years).

Individual atoms, in a radioactive isotope, will decay at a random moment. The half-life refers to how long it takes for half of the atoms in a given sample to decay (and convert to some other type of isotope).

Answer 3

In Physics, there is an inverse exponential relationship between the half-life and the radioactivity of a substance.

Half-life denotes the period during which a specific substance will decrease by 1/2 through radioactive decay. It can also be described as the period during which a single radioactive atom has a 1/2 probability of decaying some time during that specific duration.

The shorter the half-life, the more radioactive that substance is. For example, a radioactive substance 'A' with a half-life of 5 days will decay twice as quickly as a substance 'B' with a half-life of 10 days.

Radioactive decay is a form of exponential decay. In the example above. if you started out with 100g of substance 'A' (half-life of 5 days) and 100 g of substance 'B' (half-life 10 days), then after 10 days, you would have 50g of substance 'B', and only 25g of substance 'A'.

Note that, in life sciences, the term 'half-life' is a pharmacalogical term, and has nothing to do with radioactive decay.

Answer 4

The rate of radioactive decay is proportional to the number of radioactive nuclei in a sample. Mathematically this is -dN/dt prop N (the negative sign indicating that this is decaying rather than increasing). A simple integration leads to a solution for the number of radioactive nuclei compared to a starting number(N0) at some time (t) later:

N = N0 exp(-lambda * t)

This type of equation is so common in physics that we often refer to it as our favourite equation.

Lambda in the equation is the "decay" constant, which describes the relationship between radioactivity (A) and number (N)

A = N * lambda

lambda = ln(2)/halflife

Now we see the halflife for the first time, which is the time taken for us to reach exactly half of the number of radioactive nuclei that we started with. This can be calculated from the first equation by sticking 1/2 in as the number, N, and 1 in as N0 and then taking logs.

Lambda is entirely dependant on half-life which is dependant on the nuclide. The simple relationship between N, lambda and A means that the same equation for N can be used for A:

A = A0 exp(-lambda * t)

This is more convenient than the number equation because we can measure the actual radioactivity but it can be difficult (!) to count the exact number of nuclei in a large sample.

Answer 5

If you know the half life of an isotope and the amount of it present, it is possible to calculate the numbers of decay events per second in the mass. This does not provide all the information about radioactivity, because it does not provide information about the type of decay. The missing information includes the type of emission (alpha, beta, gamma, fission, etc.), the energy of the emitted particle or particles, and the energy imparted to the atom itself.

Another piece of information that needs to be accounted for is the isotope of the daughter atom or atoms. If these are inert, the radioactivity declines. But if the daughter atoms are radioactive, they may make the mass more radioactive, increasing the number of decay events per second, and change its nature by making different emissions of their own.

Answer 6

Radioactive decay is the process where unstable nuclei release energy and particles in order to reach a lower energy state.

Half-life, on the other hand, is the period of time where one half of the population of nuclei achieve radioactive decay.