Answer to Question #160169 in Atomic and Nuclear Physics for Ivo

Question

A sample of radioactive material contains 1.00 x 10^15 atoms and has an activity of 6.00 x 10^11 Bq. What is it's half-life?

Answer 1

The relationship between the activity $R$ and the number of nuclei in the sample, $N$, can be written as follows:

$$R=N\lambda,$$

here, $\lambda$ is decay constant.

Then, from this formula we can find the decay constant:

$$\lambda=\dfrac{R}{N}.$$

The relationship between the half-life of a sample, $T_{1/2}$, and its decay constant $\lambda$ can be written as follows:

$$T_{1/2}=\dfrac{ln2}{\lambda}.$$

Substituting $\lambda$ into the previous formula, we get:

$$T_{1/2}=\dfrac{Rln2}{N}=\dfrac{1.0\cdot10^{15}\cdot ln2}{6.0\cdot10^{11}\ Bq}=1.16\cdot10^3\ s=19.3\ min.$$