Vernier Software & Technology

# Determining the Half-Life of an Isotope

## Introduction

One type of nuclear reaction is called radioactive decay, in which an unstable isotope of an element changes spontaneously and emits radiation. The mathematical description of this process is shown below.

$R(t) = {R_0}{e^{ - \lambda t}}$

In this equation, λ is the decay constant, commonly measured in s–1 (or another appropriate unit of reciprocal time) similar to the rate law constant, k, in kinetics analyses. R0 is the activity (rate of decay) at t = 0. The SI unit of activity is the bequerel (Bq), defined as one decay per second. This equation shows that radioactive decay is a first-order kinetic process.

One important measure of the rate at which a radioactive substance decays is called half-life, or t1/2. Half-life is the amount of time needed for one half of a given quantity of a substance to decay. Half-lives as short as 10–6 second and as long as 109 years are common.

In this experiment, you will use a source called an isogenerator to produce a sample of radioactive barium. The isogenerator contains cesium-137, which decays to produce barium-137. The newly made barium nucleus is initially in a long-lived excited state, which eventually decays by emitting a gamma photon and becomes stable. By measuring the decay of a sample of barium-137, you will be able to calculate its half-life.

Follow all local procedures for handling radioactive materials. Follow any special use instructions included with your isogenerator.

## Objectives

In this experiment, you will

• Use an isogenerator to produce radioactive barium-137 for analysis.
• Use a radiation counter to measure the decay of a sample of barium-137.
• Calculate the decay constant and half-life of barium-137.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

### Option 2

You may also need an interface and software for data collection. What do I need for data collection?

## Advanced Chemistry with Vernier

See other experiments from the lab book.

 1 The Determination of a Chemical Formula 2 The Determination of the Percent Water in a Compound 3 The Molar Mass of a Volatile Liquid 4 Using Freezing-Point Depression to Find Molecular Weight 5 The Molar Volume of a Gas 6 Standardizing a Solution of Sodium Hydroxide 7 Acid-Base Titration 8 An Oxidation-Reduction Titration: The Reaction of Fe2+ and Ce4+ 9 Determining the Mole Ratios in a Chemical Reaction 10 The Determination of an Equilibrium Constant 11 Investigating Indicators 12 The Decomposition of Hydrogen Peroxide 13 Determining the Enthalpy of a Chemical Reaction 14A Separation and Qualitative Analysis of Cations 14B Separation and Qualitative Analysis of Anions 15A The Synthesis of Alum 15B The Analysis of Alum 16 Conductimetric Titration and Gravimetric Determination of a Precipitate 17 Determining the Concentration of a Solution: Beer's Law 18 Liquid Chromatography 19 Buffers 20 Electrochemistry: Voltaic Cells 21 Electroplating 22 The Synthesis and Analysis of Aspirin 23 Determining the Ksp of Calcium Hydroxide 24 Determining Ka by the Half-Titration of a Weak Acid 25 The Rate and Order of a Chemical Reaction 26 The Enthalpy of Neutralization of Phosphoric Acid 27 α, β, and γ 28 Radiation Shielding 29 The Base Hydrolysis of Ethyl Acetate 30 Exploring the Properties of Gases 31 Determining Avogadro's Number 32 Potentiometric Titration of Hydrogen Peroxide 33 Determining the Half-Life of an Isotope 34 Vapor Pressure and Heat of Vaporization 35 Rate Determination and Activation Energy

### Experiment 33 from Advanced Chemistry with Vernier Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.