radioactive isotopes most commonly decay by emitting an alpha or beta
particle. In most decay processes, the product instantly relaxes to a more stable nuclear
configuration by emitting a gamma ray, and thus the alpha or beta radiation is accompanied by
simultaneous gamma radiation. However, in the case of barium-137 (produced by a beta decay
process), this relaxation takes longer, and thus the gamma decay can be observed as a reaction
on its own. The reaction is represented by:
137Ba* --> 137Ba + γ
where the * denotes a high energy state.
Most radioactive decay obeys first order kinetics and therefore the half-life of a radioisotope is
independent of its concentration. In this experiment, you will be studying the decay of
metastable barium-137 to determine if it is in fact first order. Once the order of the reaction is
known, you can calculate the rate constant and, if it is first order, the half life.
the end of your six minutes, the number on the screen is the total number over the entire six
minute period. You, however, want only those events which happened in each thirty second
time interval, so you must calculate those values. You also must correct for the background
radiation, which you do not want to include in your final calculations. Lastly, at some point the
rate of the reaction will fall to a point where it is no longer detectable – if that point is reached
within the six minutes that you are collecting data, some of your final numbers will need to be
discarded, or else you will not get a graph that looks linear.
Once you know the decay events for each 30 second interval, determine the order of
the reaction by finding the integrated rate law that most closely approximates a straight line
when graphed. For simplicity, you can use the decay events themselves without first converting
to concentration. Furthermore, you only need to consider zeroth, first, and second order
perfectly linear, but using Excel to calculate the R value for a line of best fit will tell you which
graph is the best. From this graph you can calculate your rate constant. If it is first order, you
can also calculate the half-life.
- If the reaction is zeroth order or second order, you can not calculate the half life. Explain why this is.
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