Vernier Software and Technology
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 1

Option 2

Additional Requirements

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

Standards Correlations

See all standards correlations for Advanced Chemistry with Vernier »

Advanced Chemistry with Vernier

See other experiments from the lab book.

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

Experiment 33 from Advanced Chemistry with Vernier Lab Book

<i>Advanced Chemistry with Vernier</i> book cover

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