## Decay Constant and Radioactivity

The relationship between **half-life** and the amount of a radionuclide required to give an activity of one curie is shown in the figure. This amount of material can be calculated using **λ**, which is the **decay constant** of certain nuclide:

The following figure illustrates the amount of material necessary for **1 curie** of radioactivity. It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. Of course, the longer lived substance will remain radioactive for a much longer time. As can be seen, the amount of material necessary for 1 curie of radioactivity can vary from an amount too small to be seen (0.00088 gram of cobalt-60), through 1 gram of radium-226, to almost three tons of uranium-238.

## Example – Calculation of Radioactivity

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

**Calculate:**

- The number of iodine-131 atoms initially present.
- The activity of the iodine-131 in curies.
- The number of iodine-131 atoms that will remain in 50 days.
- The time it will take for the activity to reach 0.1 mCi.

**Solution:**

- The number of atoms of iodine-131 can be determined using isotopic mass as below.

**N**_{I-131}** = m**_{I-131}** . N**_{A}** / M**_{I-131}

**N**_{I-131 }**= (1 μg) x (6.02×10**^{23}** nuclei/mol) / (130.91 g/mol)**

**N**_{I-131}** = 4.6 x 10**^{15}** nuclei**

- The activity of the iodine-131 in curies can be determined using its
**decay constant**:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_{50d}) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2^{10} = 1024) is widely used to define residual activity.

We hope, this article, **Calculation of Radioactivity from Decay Constant**, helps you. If so, **give us a like** in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about radiation and dosimeters.