Name:Dr. Julie J. Nazareth
Lab Partner(s):Physics 123L
Half Life of Barium-137m
Carefully follow the “set-up” procedure found on page 3 of your lab manual. Make sure you set the timer to “PULSE” at the conclusion of the warm-up. We will be doing parts A and B of the lab experiment, but not part C. Do not get the Barium-137m from the instructor until you have completed the warm-up and calibration (Part A) because the Barium-137m is short-lived.
Part A: CalibrationTable 1: Background Radiation Level
Background Counts during 5 minutes (counts) / Background Radiation Level **
** Background Radiation Level = Background Counts during 5 minutes/10
Part B: Barium Measurement
Once you start the stop watch in this part, let it run continuously. The ‘manual’ buttom is a toggle switch that alternatively starts and stops the counter. Push the ‘reset’ button to reset the counts to 0. You will be taking data for alternate half minute intervals for 10 minutes or until the sample has approximately 50 counts/half minute.Table 2: Barium Measurement
Elapsed Time, t (min.)
*** / Activity, Aunc (counts/half minute) / Corrected Activity, A (counts/half minute) +++ / ln A (ln counts)
*** Elapsed time since beginning of 30 second measurement interval.
+++ Corrected Activity = Barium Activity – Background Radiation Level
### Only fill out this column if you do NOT have semi-log graph paper for the plot of corrected activity versus elapsed time.
Graph and Calculations
(Step #1) Graph. On semi-log paper plot Corrected Activity versus Elapsed Time. Put the Corrected Activity on the vertical, logarithmic scale, and elapsed time in minutes on the horizontal, linear scale. Draw a best fit straight line. If you do not have semi-log paper, simply calculate the natural log of the Corrected Activity (fill in the last column in Table 2) and plot ln(Corrected Activity) versus Elapsed Time on regular graph paper.
(Step #2) Find the experimental half life of Barium-137m. Select two convenient activity points on your best fit line that are NOT data points AND for which the first (earlier) activity has twice the counts as the second (later) activity. Draw a vertical line down the time (horizontal) axis for both activities and note the two times. The difference between these two times is your measured half life for Barium-137m. [If your graph is plotted on regular (linear) graph paper, you will have to do a little bit of work to figure out where the second (later) activity is half the first. Choose a convenient first (earlier) point on your graph (say ln A = 5.0). Take the anti-ln (= ex button) of that activity using your calculator (anti-ln 5.0 = 148.4). Divide the result in half (148.4/2 = 74.2). Take the ln of that number (ln 74.2 = 4.3). Find that ln on your best fit straight line – this is your second point. Draw the lines down to the time axis as described above. The half life is the difference between these two times.]
(Step #3) Find the experimental decay constant for Barium-137m from the slope of your graph. [Hint: Sinceln A is proportional to -λt, the slope = -λ.]
Calculate the accepted value for the decay constant, λ, in the space provided below. Use equation 6 and the accepted value for the half life (found in Table 3).
λ =Table 3: Comparing Results of Graph of ln(A) vs t to Accepted Values
Graph / Accepted Value / Percent difference (%)
Half Life, t½ (min.) / 2.55
Decay Constant, λ(min.-1)
Half Life % Error = graph – accepted x 100% =
Decay Constant % Error = graph – accepted x 100% =
Question: Answer question 5 from the lab manual on a separate sheet of paper. Show all work.
Don’t forget to write your summary! (Remember, start with introductory sentence stating the purpose of the experiment. Some things to consider … how does the half life determined from the graph compare to the accepted value? If the percent difference is not small, what could you do to obtain better results? How does the decay constant determined from your graph compare to the accepted value (from equation 6)? If the percent difference is not small, what could you do to obtain better results?)
Lab: Half Life of Barium-137mUpdated 5/14/09