Difference between revisions of "Radioactive Disintegration (Introduction to Radiochemistry)"
(Created page with "Radioactive disintegration is a stochastic proces, which means a random process, that can be described statistically. In this task you will learn about the secular radioactive eq...") |
|||
| Line 1: | Line 1: | ||
| − | Radioactive disintegration is a stochastic proces, which means a random process, that can be described statistically. In this task you will learn about the secular radioactive equilibrium, and how any measure of a radioactive source is stated with uncertainty. <br> | + | Radioactive disintegration is a stochastic proces, which means a random process, that can be described statistically. In this task you will learn about the secular radioactive equilibrium, and how any measure of a radioactive source is stated with uncertainty. <br> |
| − | In a sample with N radioactive atoms of a particular nuclide, the number of atoms that disintegrates with the time ''dt ''will be proportional with N, see the formula below. | + | In a sample with N radioactive atoms of a particular nuclide, the number of atoms that disintegrates with the time ''dt ''will be proportional with N, see the formula below. |
| − | <math>-\frac{dN}{dt} = \lambda N \rightarrow \lambda N = A</math>, | + | <math>-\frac{dN}{dt} = \lambda N \rightarrow \lambda N = A</math>, |
| − | where < | + | where <span class="texhtml">λ</span> is the disintegration constant and A is the rate of disintegration. |
| − | + | The above equation can be solved into the following: | |
| + | |||
| + | <math>N_{t} = N_{0} e^{-\lambda t}</math> | ||
| + | |||
| + | N<sub>0</sub> is the number of atoms of the nuclide at hand present at t = 0. The time past when half of the nuclides has disintegrated is called the half-life. <math>N = \frac{N_{0}}{2}</math> can be placed into equation 1.1 to give the following connection between the disintegration constant and the half-life: | ||
| + | |||
| + | <math>\lambda = \frac{ln2}{T_{1/2}}</math> | ||
| + | |||
| + | The half-life is a characteristic value for each radioactive nuclide. A radioactive nuclide will often disintegrate into a product that <br> | ||
Revision as of 12:17, 2 July 2012
Radioactive disintegration is a stochastic proces, which means a random process, that can be described statistically. In this task you will learn about the secular radioactive equilibrium, and how any measure of a radioactive source is stated with uncertainty.
In a sample with N radioactive atoms of a particular nuclide, the number of atoms that disintegrates with the time dt will be proportional with N, see the formula below.
,
where λ is the disintegration constant and A is the rate of disintegration.
The above equation can be solved into the following:
N0 is the number of atoms of the nuclide at hand present at t = 0. The time past when half of the nuclides has disintegrated is called the half-life. can be placed into equation 1.1 to give the following connection between the disintegration constant and the half-life:
The half-life is a characteristic value for each radioactive nuclide. A radioactive nuclide will often disintegrate into a product that
