**Examples for radioactivity**

Example #1

Problem:

One mole of radioactive atoms has a half life of 100 years. After 7500 years, what is the number of atoms that remain?

Solution:

First find the decay constant, **l**, in inverse years
using **l **= 0.693/t_{1/2}. Then the number left is Avogadro's number times
exp(-**l***7500)

16

Example #2

Problem:

One measures 50,000 decays of a radioactive sample in 20 seconds. One measures the same sample 50 days later and observes only 10,000 decays in 20 seconds. What is the half life of the radioactivity.

Solution:

Since the number of decays in a given time interval are proportional to the number of undecayed nuclei, one knows that one fifth of the original nuclei still exist after 50 days. One can then state

where the time * t *is
50 days. One can then solve for the half life by taking the natural logarithm of both
sides of the equation.

t_{1/2} = 21.5 days

Example #3

Problem:

A beam of 8.0 *MeV* protons is aimed
at a rat whose mass is 2.0 *kg*. If the RBE of the radiation is 10 and the
biologically equivalent dose absorbed by the rat is 250 *rems*, how many protons
did the rat absorb?

Solution:

The dose is: 250 *rems* = (Energy of a proton in
Joules / 0.01) *(number of protons)*RBE/(mass of rat). After converting the energy of 8 *MeV*
into Joules, one can solve the above equation for the number of protons.

* N* = 3.9 E11