Lifetime Measurement

Introduction

The activity (in decays per second) of some radioactive samples varies in time in a particularly simple way. If the activity (R) in decays per second of a sample is proportional to the amount of radioactive material (R ∝ N, where N is the number of radioactive nuclei), then the activity must decrease in time exponentially:

In this equation λ is the decay constant, commonly measured in s^–1 or min^–1. R₀ is the activity at t = 0. The SI unit of activity is the becquerel (Bq), defined as one decay per second.

You will use a source called an isogenerator to produce a sample of radioactive barium. The isogenerator contains cesium-137, which decays to barium-137. The newly made barium nucleus is initially in a long-lived excited state, which eventually decays by emitting a gamma photon. The barium nucleus is then stable, and does not emit further radiation. Using a chemical separation process, the isogenerator allows you to remove a sample of barium from the cesium-barium mixture. Some of the barium you remove will still be in the excited state and will subsequently decay. It is the activity and lifetime of the excited barium you will measure.

Objectives

In this experiment, you will

• Use a radiation counter to measure the decay constant and half-life of barium-137.
• Determine if the observed time-variation of radiation from a sample of barium-137 is consistent with simple radioactive decay.