Radioactive Half-life of Barium-137m
...y rate of one spontaneous nuclear transition per second. The Curie (Ci) is still most often used as the unit for activity and the conversion between these two are 1 Ci = 3.7E10 Bq. Nuclear half-life (ô), the time it takes the activity of a radioactive sample to decrease by half its original activity, is used to help identify unknown isotopes. It depends on the decay rate constant so that the larger the decay rate, the smaller the half-life. If the initial activity is Ao at time t = 0, then the activity at time t = ô will be A= ½ Ao and the following equation will be true: ½ Ao = Ao*e-ëô. By simplifying and taking the natural logarithm of each side, the equation becomes ô = ln2/ë. Since ln2 is 0.693, then the nuclear half life can be computed from a measurement of the decay rate constant ë, and the equation is as follows: ô = 0.693/ë. When a quantity N decreases exponentially with time t as the activity A of a radioactive sample does, a plot of ln(N) versus t will result in points that lie along a straight line. The equation for this straight line will be of the form, N = Noe-ëô, and the decay rate constant ë characterizes how fast the quantity N or A changes with time and is different for varying radioactive isotopes. Taking the natural log of N you get this simplified equation: lnN = lnNo – ëô. This is an equation for a straight line in the form y= a + bx, where y = ln N, a = lnNo, x = t, and b = -ë. The rate constant, ë, may be found from a plot of ln N versus t and linear regression. Procedure: The apparatus used in this experiment consisted of a Nucleus scaler/time, Geiger-Mueller tube with stand and source holder, a cesium/barium-137m isogenerator, planchet, a source holder tray, Pasco Science Workshop 750 data interface, Pasco Science Workshop software, Excel software, and a computer system. Before starting the experiment, we made several preparations to the set up system. The high voltage on the scaler/timer unit of the Geiger-Mueller tube was set to 900 volts, and the power was switched on and initialized to zero. An Excel spreadsheet was opened and set up as instructed in the lab manual example. A background measurement was made with all the sources removed from the area of the detector. The preset time on the scaler/timer unit was set to ten minutes and the scaler was started. The number of background counts (NT) was recorded into the spreadsheet and the number of counts per 30 second period (NB) was computed and recorded as well. Once this was done, the data studio system was set up for the experiment with all the proper parameters. To measure the activity of the Ba-137m sample as a function of time, the particles were counted in thirty second intervals for a total of fifteen minutes. The scaler was initialized again and reset back to zero. When the TA gave us our sample, we immediately turned on the “count” button on the scaler and let it run for the fifteen minutes. All...