RESULTS AND CALCULATIONS

Determination of the half-life of Barium-137m.

  1. Write the appropriate nuclear equations to illustrate the decay sequence for Cs137/Ba137m/Ba137.
  2. Correct all recorded counts for background.
  3. Plot the corrected cpm vs. time in your lab notebook. The points should be placed half-way through the first, third, fifth etc. minutes.
  4. From your graphs select two activities which show the earlier count rate twice as active as the later count rate. Draw perpendiculars from these points to each axis and determine the half-life of the Ba-137m. Repeat this with other sets of count rates to verify that half-life is a constant for a particular radioactive substance.
  5. In addition to a graphic determination, the half-life of a radioisotope can be determined mathematically.
Mathematically the number of radioactive atoms in a sample decreases exponentially: where

l - decay constant

t - elapsed time between counts

At and Ao - represent activity in cpm at time t and starting time 0.

Once the value of l is known the half-life may be calculated by using the expression:

Using sets of data collected for Ao, At and t compute the decay constant (l ) and the half-life of Barium-137m. Your most reliable determination of half-life should be an average of several calculations.