Name:
Lab Partner(s):
Date:
Dr. Julie J. Nazareth
Physics 123L
Section:
Half Life of Barium-137m
Part A: Calibration
Table 1: Background Radiation Level
Background Counts
Background Radiation
during 5 minutes
Level **
(counts)
(counts/half minute)
** Background Radiation Level = Background Counts during 5 minutes/10
Part B: Barium Measurement
Do not get the Barium-137 from the instructor until you are ready to start!
Once you start the stop-watch in this part, let it run continuously until the end.
Table 2: Barium Measurement
Elapsed Time,
Activity, Aunc
Corrected Activity, A
Natural log of Corrected
t (min.) ***
(counts/half minute) (counts/half minute) +++ Activity, ln A (ln counts)
0
1
2
3
4
5
6
7
8
9
10
*** Elapsed time since beginning of 30 second measurement interval.
+++ Corrected Activity = Barium Activity – Background Radiation Level
Graph: Graph the natural log of the corrected activity versus the elapsed time (“y” vs “x’) on
graph paper. Draw a best fit line to your data. Title and label your graph appropriately, as usual.
The y-axis is unitless (because of the natural log), but the x-axis does have units (minutes).
Circle, box or “x” your chosen slope points (remember, not data points!). Calculate the slope of
your graph. A shared graph is allowed within a lab group if signed off by the instructor by
the end of the lab period. The slope calculation MUST be on the graph if it is a shared
graph.
Analysis of graph #1: Find the experimental decay constant for Barium-137m from the slope of
your graph. [Hint: Since ln A is directly proportional to -λt, the slope = -λ, so λexp = -slope.]
Put the result in Table 3.
Lab: Half Life of Barium-137m
Updated 5/19/17
Analysis of graph #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 to 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. Mark
the half life on your graph. Since 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.
Follow the following steps if you need help figuring this out …
Step 1: Choose a convenient (accurate and easy to read) first (earlier) point on your line.
ln A1 = First point = __________
x
Step 2: Take the anti-ln (= e button) of that activity using your calculator.
A1 = __________
Step 3: Divide the result in half.
A2 = ½ (A1) = ___________
Step 4: Take the natural log of that number (A2)
ln (A2) = __________
Step 5: Find that ln on your best fit straight line – this is your second point.
ln A2 = Second point = __________
Step 6: Draw the lines down to the time axis as described above …
Calculations: Show the following calculations. Don’t forget units!
• Slope of the graph (may be shown on the graph)
•
Accepted value for the decay constant, λ, using the accepted value for the half life and
equation 6.
•
Percent error in the half life
•
Percent error in the decay constant
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)
Question: Answer question 5 from the lab manual on a separate sheet of paper. Show all work.
Don’t forget units for the final answer(s).
Don’t forget to write your Conclusion! (Some things to consider: Purpose of lab? 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-137m
Updated 5/19/17