Lab 8 Radiation Procedure

GEORGIA MILITARY COLLEGE

NATURAL SCIENCE DEPARTMENT

ONLINE CAMPUS

LABORATORY 8 – RADIATION

NAME

STUDENT NUMBER

CLASS

PROFESSOR’S TITLE AND NAME

Introduction

This laboratory explored the concept of radioactive decay. Radioactive decay is the process by which unstable atomic nuclei undergo radiation, emitting energy and other elements in the process (Lofts & Evergreen, 2023). Materials with unstable atomic nuclei are radioactive materials. An important benefit of radioactive decay is its use in dating samples to determine when they lived on earth and make predictions on the conditions on earth at the time. Carbon-14 is a radioactive isotope of the element carbon that is commonly used to estimate the age of organisms through the process of radiocarbon dating. Carbon-14 is formed in the environment when cosmic rays interact with nitrogen atoms (N) and nitrogen molecules (N2) (Lofts & Evergreen, 2023). It undergoes rapid oxidization in the atmosphere to form carbon (IV) oxide. Living organisms are continually replenishing their carbon-14 content by exchanging carbon (IV) oxide with the biosphere. This exchange stops when an organism dies and their carbon-14 content begins to decline over time as it undergoes radioactive decay to form Nitrogen-14 atoms (Lofts & Evergreen, 2023). Thus, the older the artefact, the lower its carbon-14 concentration. The process of determining an artefact’s age by examining its carbon-14 content is referred to as radiocarbon dating.

The number of caron-14 atoms decaying per unit of time is referred to as the rate of radioactive decay. It is calculated using the formula:

Rate of radioactive decay = k Nt …………………………………………….equation 1

Where Nt is the number of radioactive atoms in the sample at time t, and k is the radioactive decay constant.

The time it takes for one half of the radioactive atoms to decay is defined as the artefact’s half-life (denoted as t1/2). It is calculated as:

T1/2 = ln2/k………………………………………………equation 2

T1/2 = 0.693/k; where k is the radioactive decay constant.

Carbon-14 has a half-life of 5,730 years. This implies that concentration of carbon-14 in an artefact is halved over the course of 5,730 years. This laboratory seeks to use actual data from an experiment to determine the age of sampled artifacts. It has two primary objectives:

i) To understand the concepts of radioactive decay and half-life.

ii) To familiarize with the half-life curve.

Materials and Methods

Preparing the Lab

i) Access the simulation environment through the ‘Radioactive Dating Game’ tab on the course home page.

ii) On the simulation environment, choose the ‘Half Life’ tab and click on ‘Carbon-14’ from the right menu.

iii) Examine the graph that loads and record the estimated half-life. At this point, one has all they need to perform the lab.

Performing the Lab

iv) From the bucket, select and move 10 carbon-14 atoms to the workspace to examine how many of these will undergo radioactive decay until the half-life point. Record this number in table 1 below.

v) Repeat step (IV) above with 20, 30, and 40 carbon-14 atoms.

vi) Return to the bucket, select uranium, and move 10 atoms to the workspace. Record the estimated half-life from the graph, examine and record how many atoms decay before the half-life point.

vii) Repeat step (VI) above using 20, 30 and 40 atoms.

Data Collection Part One

viii) Calculate the average Nt value for both Carbon-14 and Uranium and record in table 1 below.

ix) Use the half-life equation above (equation ii) to obtain the decay constant and record the values in table 2 below.

x) Using equation (I), calculate the rate of decay for each element and record the values in the table 2 below.

Data Collection Part Two

xi) On the simulation environment, select ‘Dating Game.’ This phase of data collection seeks to use carbon dating to determine the age of various samples.

xii) On the list of samples, drag the probe to the ‘Living tree’ sample until a dialogue box appears that contains the carbon percentage in the sample. Record this value in table 3 below.

xiii) Repeat step (xii) for the other 5 samples – Animal Skull, Wooden Cup, Bone, Fishbone and Rock 5.

Data Analysis

xiv) Use the percentage of carbon present in the sample to predict the sample’s age.

xv) Prepare a report for the observations made.

Data and Discussion

Data

Table 1

Nt

Estimated t1/2 (Years)

10 atoms

20 atoms

30 atoms

40 atoms

Average

Carbon-14

Uranium- 238

4.608 x 109

Table 2: Half-Life and Rate of Decay

Decay Constant

Rate of Decay

Carbon-14

0.000121 years

0.000484 atoms per year

Uranium -238

1.54 x 20-10

6.93 x 10-10

Table 3: Age Determination through radiocarbon Dating

Sample

% Carbon Remaining

Age of Sample

Living Tree

Animal skull

Wooden Cup

Bone

Fish bones

Rock 5

Not sure

Discussion

The data in table 1 seeks to examine how the half-life changes with the mass of an element. The results indicate that the half-life of both Carbon-14 and Uranium-238 remains constant regardless of the number of atoms of the sample. This indicates that the half-life is independent of an element’s mass. This is because the decay process is a radioactive process that that does not depend on the elements’ stoichiometric properties. The half-life is based purely on the configuration of neutrons and protons in an isotope’s nucleus. These determine the nucleus’ stability and hence, the probability that radioactive decay will occur. However, comparing the two isotopes by rate of decay in table 2, Uranium-238 decays at a slower rate than carbon-14 and thus, has a longer half-life. This is because its nucleus is more stable than carbon-14 and disintegrates at a lower rate.

As hypothesized at the start of the lab, the results in table 3 indicate an inverse relationship between carbon concentration and age. Samples with lower carbon concentrations are generally older since carbon-14 decays with time, and reduces in concentration as an artefact ages after death. The fish bone sample has the least concentration of carbon and is predicted to be aged over 16,000 years. The Living Tree records 100 percent concentration of carbon-14 because living plants are continually replenishing their carbon-14 supply through uptake of carbon (IV) oxide for photosynthesis. The carbon decay process only begins when an organism dies and stops exchanging carbon-14 with the biosphere.