Experiment 1 Determining the half-life of Ba−137

Experiment 1

Determining the half-life of Ba−137

Objective

:

1. Studying how activity of a radioactive source changes with time.

2. Determining the half-life of Ba−137m Theory:

If there are radioactive nuclei of a certain kind in a sample, the decay probability is the same for each nucleus. However, the instant at which an

individual nucleus decays cannot be predicted. If no further radioactive nuclei are supplied, the number N of a particular kind of nuclei decreases during the

subsequent time interval dt by

𝑑𝑁 = −𝜆 𝑁 𝑑𝑡

Where  is a constant is called the decay constant.The decay law for the number N thereforeis:

N(t) = 𝑁_𝑜𝑒^{−𝜆 𝑡} (1)

Where 𝑁_𝑜: number of radioactive nuclei at the time t = 0. From this equation we can see that the number of nuclei will decrease to have its original value when:

N(t)

𝑁_o = 𝑒^{−𝜆 𝑡} = 1 2

i.e. when 𝑡 = ^{ln 2}_ . We call this time the half life of the radioactive sample (see fig 1).

𝑡_1/2 = ^{ln 2}_ (2)

2

For the activity of the sample, i. e., the number of decays per unit time (the rate of decay):

𝐴(𝑡) = − 𝑑𝑁

𝑑𝑡 = 𝑁(𝑡) From this it follows that:

𝐴(𝑡) = 𝐴_𝑜𝑒^{−𝜆 𝑡} (3)

Where 𝐴_𝑜 =𝑁_𝑜. i. e., the activity A(t) is also halved each time a half-life has passed.

In this experiment, the decay curve of the metastable state Ba−137m of the isotope Ba−137 is recorded and the half-life is determined. Ba−137 is a decay product of the long-lived parent substance Cs−137, whose half-life is approx. 30 years. Cs−137 decays into Ba−137 whereby  radiation is emitted. In 95 % of the decays, this is a transition into the metastable state Ba−137m (see Fig. 2), which passes into the ground state of Ba−137 via  decay with a half-life of only 2.551 min. The parent substance is stored in a Cs/Ba−137m isotope generator. The metastable isotopes Ba−137m produced in the  decay of Cs−137 are eluted from the isotope generator with an acidified sodium chloride solution at the beginning of the experiment. Then the activity of the elute is recorded.

Note that we will not be measuring the absolute activity of the eluted sample but instead a certain fraction of it that we will call the count rate (𝐼), but

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since this count rate is proportional to the absolute activity (𝐼 = 𝜀𝐴), equation (3) holds for the count rate and we can use it to find the half life of Ba-137. Ie:

𝐼(𝑡) = 𝐼_𝑜𝑒^{−𝜆 𝑡} (4) And

ln 𝐼 = −𝜆𝑡 + ln 𝐼_𝑜 (5)

Apparatus:

Geiger tube.

Counter.

Cs/Ba−137m isotope generator Stand with rod and universal clamps.

Glass test tube and glass beaker.

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Procedure:

1. Attach the universal clamps to the stand rod and clamp the end-window Geiger tube in the lower universal clamp so that it is directed upwards and remove the protective cap of the Geiger tube.

2. Clamp a test tube in the upper universal clamp so that its distance from the entrance window is approx. 0.5 cm.

3. Connect the Geiger tube to the counter and turn on the counter.

4. Measure the background activity (or in our case, the count rate) for 30 second 𝐼_𝐵𝐺 two times and find the average.

5. Follow the instructions of your lab instructor to elute the sample.

6. Immediately start counting (start the counter, then start your timer as you freeze the screen for your first reading) and record the count every 30 seconds until 10 minutes have passed, using the screen freezing feature in the device.

7. The count that you read from the counter is the accumulative count rate 𝐼_𝑎𝑐 . For any n reading of 𝐼_𝑎𝑐 , the actual count rate recorded during the 30 seconds will be 𝐼_30(𝑛) = 𝐼_{𝑎𝑐(𝑛)} − 𝐼_{𝑎𝑐(𝑛−1)} .

8. Subtract the 𝐼_𝐵𝐺 from 𝐼₃₀ and Find the count rate per one second 𝐼 for each reading.

9. Draw a graph of ln (𝐼) on y-axis vs t (time) on x-axis, and find the half-life from it using eq(5) and eq(2).

10. Find percentage error using 𝑡_{(1/2)𝑇ℎ𝑒𝑜}= 2.551 min.

Safety precautions:

1. Wear gloves and lab coat when eluting the Ba- 137 and be careful not to spell any of the elute on yourself or anyone else or on any surface. If a spell happens on a person take of the lab coat or wash the spell on clothes with water and soap. If a spell happens on a surface clean it with a tissue and discard. Don’t worry, the the Ba sample will lose almost all activity within 30 minutes.

2. After finishing with the eluted sample, discard in sink and flush with plenty of water.

3. Never touch any source using bare hands. Always use forceps to handle sources.

4. Do not eat or drink during the lab.

5. Practice ALARA by being as far away from the sources as possible and returning the source to your instructor as soon as you are finished with it and also by using appropriate shielding.

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Data sheet

Experiment 5: Determining the half-life of Ba−137

IB.G. = (... + ……... )/2 = ………… (particles per 30 seconds)

t (min) 𝐼_𝑎𝑐

(accumulative)

𝐼₃₀

(/30 s)

𝐼 = ^{𝐼30−𝐼𝐵𝐺}

30

(……..) ln 𝐼 0

0.5 1 1.5

2 2.5

3 3.5

4 4.5

5 5.5

6 6.5

7 7.5

8 8.5

9 9.5

10 10.5

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Calculations and results:

Half life from ln 𝐼 𝑣𝑠 t graph:

- Slope =

- Decay constant = 𝜆 = - 𝑡¹

2 =

- % 𝑒𝑟𝑟𝑜𝑟 =

Post lab questions:

1. If you keep repeating the experiment using the same source during close intervals of time, Will get the same average count readings? Will you get closer to the ideal half-life value of the Ba−137m?

2. Is it safe to dispose of the remaining elute in the lab sink drain? Explain why or why not