State what is meant by the decay constant of a radioactive isotope.
Show that the decay constant 
and the half-life 
of an isotope are related by the expression
In order to determine the half-life of a sample of a radioactive isotope, a student measures the count rate near to the sample, as illustrated in the figure below.
Initially, the measured count rate is 538 per minute. After a time of 8.0 hours, the measured count rate is 228 per minute. Use these data to estimate the half-life of the isotope
