An Experiment to Find the Half-Life of Aluminium-28
Abstract:
Finding the half-life of Aluminum-28 is the purpose of this lab. The class met at the Radiation Center and exposed small amounts of aluminum to energetic neutrons and watched the samples decay. After creating a table with background count and gross counts of the aluminum remaining at fifteen different one-minute intervals, this allowed the net counts per minute at each interval to be found as well. Next a graph of the net cpm verses time was plotted. After each interval was plotted the K-value (slope) was found along with the half-life. The actual half-life of Aluminum is 2.25 minutes. The half-life found in our group was 2.23 minutes.
Procedure:
The procedure is as follows on pages 63-67 of the Chemistry Laboratory Manual. No changes were made to this procedure.
Data:
Background in 30 minutes = 553
Counts per minute (cpm) = 18.45
Time Gross Counts Time Gross cpm Bk cpm Net cpm
1 2203 .2 min 11015 18.45 10996.5
2 1662 .2 min 8310 18.45 8291.5
3 1288 .2 min 6440 18.45 6421.5
4 946 .2 min 4730 18.45 4711.5
5 734 .2 min 3670 18.45 3651.5
6 540 .2 min 2700 18.45 2681.5
7 425 .2 min 2125 18.45 2106.5
8 325 .2 min 1625 18.45 1606.5
9 238 .2 min 1190 18.45 1171.5
10 183 .2 min 915 18.45 896.5
11 132 .2 min 660 18.45 641.5
12 78 .2 min 390 18.45 371.5
13 75 .2 min 375 18.45 356.5
14 64 .2 min 320 18.45 301.5
15 43 .2 min 215 18.45 196.5
Calculations:
Calculating Gross cpm example (at time 1)
Gross cpm = gross count (y) x 5
Gross cpm = 2203 x 5
Gross cpm = 11015
Calculating Net cpm example (at time 2)
Net cpm = gross cpm – background cpm
Net cpm = Gross cpm – 18.45
Net cpm = 11015 – 18.45
Net cpm = 10996.57
Find the slope from paper graph:
K = slope
K= [ln(net cpm12)- ln(net cpm2)] / [t12-t2]
K = [ln(371.55) – ln(8291.57)] / (12-2)
K = .3105 min
Calculating Half-life from estimated K-value
T1/2= ln2 K
T1/2=2.23
Graph of ln(cpm) versus time:
Calculating slope
Finding the half-life of Aluminum-28 is the purpose of this lab. The class met at the Radiation Center and exposed small amounts of aluminum to energetic neutrons and watched the samples decay. After creating a table with background count and gross counts of the aluminum remaining at fifteen different one-minute intervals, this allowed the net counts per minute at each interval to be found as well. Next a graph of the net cpm verses time was plotted. After each interval was plotted the K-value (slope) was found along with the half-life. The actual half-life of Aluminum is 2.25 minutes. The half-life found in our group was 2.23 minutes.
Procedure:
The procedure is as follows on pages 63-67 of the Chemistry Laboratory Manual. No changes were made to this procedure.
Data:
Background in 30 minutes = 553
Counts per minute (cpm) = 18.45
Time Gross Counts Time Gross cpm Bk cpm Net cpm
1 2203 .2 min 11015 18.45 10996.5
2 1662 .2 min 8310 18.45 8291.5
3 1288 .2 min 6440 18.45 6421.5
4 946 .2 min 4730 18.45 4711.5
5 734 .2 min 3670 18.45 3651.5
6 540 .2 min 2700 18.45 2681.5
7 425 .2 min 2125 18.45 2106.5
8 325 .2 min 1625 18.45 1606.5
9 238 .2 min 1190 18.45 1171.5
10 183 .2 min 915 18.45 896.5
11 132 .2 min 660 18.45 641.5
12 78 .2 min 390 18.45 371.5
13 75 .2 min 375 18.45 356.5
14 64 .2 min 320 18.45 301.5
15 43 .2 min 215 18.45 196.5
Calculations:
Calculating Gross cpm example (at time 1)
Gross cpm = gross count (y) x 5
Gross cpm = 2203 x 5
Gross cpm = 11015
Calculating Net cpm example (at time 2)
Net cpm = gross cpm – background cpm
Net cpm = Gross cpm – 18.45
Net cpm = 11015 – 18.45
Net cpm = 10996.57
Find the slope from paper graph:
K = slope
K= [ln(net cpm12)- ln(net cpm2)] / [t12-t2]
K = [ln(371.55) – ln(8291.57)] / (12-2)
K = .3105 min
Calculating Half-life from estimated K-value
T1/2= ln2 K
T1/2=2.23
Graph of ln(cpm) versus time:
Calculating slope
References: CH221 Laboratory Manual Winter 2008. Haak, Margie. Myles, Daniel. Pages 63-67. Van Schandevijl, R.. "Half Life of Al-28." Journal of Radioanalytical and Nuclear Chemistry 9(1971): 55-60.