Difference between revisions of "Radioactive Disintegration (Introduction to Radiochemistry)"
Line 15: | Line 15: | ||
<math>\lambda = \frac{ln2}{T_{1/2}}</math> | <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 is radioactive as well: Nucleus 1<math>\rightarrow</math>Nucleus 2 <math>\rightarrow</math>Nucleus 3. The initial nucleus is usually referred to as the mother nuclide and the product as the daughter nuclide. <br> | + | The half-life is a characteristic value for each radioactive nuclide. A radioactive nuclide will often disintegrate into a product that is radioactive as well: Nucleus 1<math>\rightarrow</math>Nucleus 2 <math>\rightarrow</math>Nucleus 3. The initial nucleus is usually referred to as the mother nuclide and the product as the daughter nuclide. <br> |
− | Assume that at the time ''t = 0'', N<sub>0 </sub>of the mother is ''N<sub>1</sub>(t =0), N<sub>2</sub>(t=0) and N<sub>3</sub>(t=0)'', the change in number of mother- and daughter nuclides can then respectively be described through the following equations:<br> | + | Assume that at the time ''t = 0'', N<sub>0 </sub>of the mother is ''N<sub>1</sub>(t =0), N<sub>2</sub>(t=0) and N<sub>3</sub>(t=0)'', the change in number of mother- and daughter nuclides can then respectively be described through the following equations:<br> |
− | ''dN<sub>1</sub> = -< | + | ''dN<sub>1</sub> = -<span class="texhtml">λ</span>N<sub>1</sub>dt'' |
− | ''dN<sub>2</sub> = < | + | ''dN<sub>2</sub> = <span class="texhtml">λ<sub>1</sub></span>N<sub>1</sub>dt - <span class="texhtml">λ<sub>2</sub></span>N<sub>2</sub>dt'' |
− | of equation 1.1 is allready known, see e.q.1.1, while the solution of the number of daughter nuclides is given by: | + | of equation 1.1 is allready known, see e.q.1.1, while the solution of the number of daughter nuclides is given by: |
− | <math>N_{2} = \frac{\lambda_{1}}{\lambda_{2} -\lambda_{1}} N_{0}(e^{-\lambda_{1} t})</math> | + | <math>N_{2} = \frac{\lambda_{1}}{\lambda_{2} -\lambda_{1}} N_{0}(e^{-\lambda_{1} t}-e^-\lambda_{2}t) \rightarrow N_{2}= \frac{\lambda_{1}}{\lambda_{2}- +lambda_{1}}N_{1}(t)(1-e^{-(\lambda_{2}- \lambda_{1})t)</math> |
Revision as of 13:33, 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:
Nt = N0e - λt
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.
N = N0/2 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 is radioactive as well: Nucleus 1
Assume that at the time t = 0, N0 of the mother is N1(t =0), N2(t=0) and N3(t=0), the change in number of mother- and daughter nuclides can then respectively be described through the following equations:
dN1 = -λN1dt
dN2 = λ1N1dt - λ2N2dt
of equation 1.1 is allready known, see e.q.1.1, while the solution of the number of daughter nuclides is given by: