Answer to Question #191874 in Physics for John

Question

An isotope of Iodine (atomic number 53) has a mass number of 123 and a half-life of 13 hours. It decays by emitting a beta particle.

If the sample has an initial activity of 2000kBq what will be the activity

52 hours later.

Answer 1

The activity 52 hours later will be

$$A=A_0e^{-\lambda t}=A_0\exp\bigg(-\frac{\ln2}{t_{1/2}}·t\bigg),\\\space\\ A=2000\exp\bigg(-\frac{\ln2}{13}·52\bigg)=125\text{ kBq}.$$