AP Physics Lab

Beta Decay of ¹³⁷Cs and the half-life of ¹³⁷Ba* by photon emission

Objective: Determine the half-life (T_½) of a radionuclide using the Geiger-Mueller counter.

Introduction

Radionuclides emit various particles and photons during their disintegration. Alpha and beta emitters decay at various rates as characterized by their decay constant, . The relationship between radioactive decay and the data collected in this lab is shown in the equation:

                                                 N = N_o e^{- lt}

where N_o is the original activity,  l is the decay constant, and t is the elapsed time.

Also, it is known that:

                                            T_½ = 0.693/ l    or    l = 0.693/ T_½

Hence, if we can measure the original and final activities of the radionuclide, we can calculate the half life and decay constant.

In this lab, ¹³⁷Cs is the parent nuclide that emits a particle and decays to ¹³⁷Ba* or ¹³⁷Ba. The half life of this transition is approximately 30 years. However, the ¹³⁷Ba* represents a metastable state that eventually emits a photon and becomes ¹³⁷Ba. It is the half-life of this transition that is the focus of this lab.

Materials: G-M counter, Apple II computer, ¹³⁷Cs source (Isogenerator Kit)

Methods and Analysis

1. Determine the background radiation (in cpm) over a three minute interval, then convert to counts per 15 second interval.

2. Extract ¹³⁷Ba* from the ¹³⁷Cs source following the methods described and place the elution onto a planchet for counting.

3. Record the count every 15 seconds on the computer for approximately 6-8 minutes.

4. Subtract the background count from each value.

5. Graph the counts vs time. Draw a smooth best-fit line.

6. Determine from the graph where the number of counts is ½ the original, then estimate the half life. Compare with the known T_½ of ¹³⁷Ba* (from the Chart of the Nuclides) and calculate a percent error. Discuss the sources of error.

7. Write the entire nuclear decay of ¹³⁷Cs to ¹³⁷Ba by beta and gamma photon emission.

8. Calculate the decay constant of the ¹³⁷Ba transition from the half-life. Compare with two other decay constants.

9. Define decay constant.

10. If the beta particle emitted by ¹³⁷Cs has a kinetic energy of 0.100 MeV, what is it's velocity and what is the recoil velocity of the ¹³⁷Cs nucleus?

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