AP Chemistry
Half Life Experiment
RADIOACTIVITY LAB SAFETY PRECAUTIONS
Today’s lab uses a sealed radioactive source. Within this minigenerator is
radioactive cesium with a half-life of about 30 years. Because this source is sealed,
you will not come into contact with this cesium unless the minigenerator is broken.
Therefore, please be careful handling this piece of equipment. The radioactive
barium that you will be working with today has a very short half-life. By the time
the lab is over today, more than 10 half-lives will have passed, at which point the
radioactivity levels are equal to the background radioactivity normally present in
the air. Therefore, this is very safe to work with as long as the following safety
precautions are followed.
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No food or drinks are allowed in this lab, please leave all food outside the lab
room.
 Safety goggles must be worn at all times when working with the radioisotope
generators.
 You must wear closed-toe shoes; no sandals may be worn.
 The eluting solution contains a weak concentration of HCl, this can cause burns
on your skin and clothing, please be careful to not spill it and goggles at all times.
 Please notify your lab instructor of any spills or accidents immediately.
 Please do not touch the sensor window face plate on the Geiger counter; this can
ruin this expensive piece of equipment.
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AP Chemistry
Introduction
 Radioactivity and Half-Lives
Radioactivity, a property of some atoms, is relevant in many areas of science. The
energy released by radioactive decay helps to keep the earth’s core molten. Radioactive
elements allow us to determine the age of geological samples. Radioactive isotopes are
used in medicine and science to visualize metabolic activities.
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But what is radioactivity?
In 1896, Henri Bacquerel discovered that uranium, when placed on a sealed, light-tight
photographic plate, exposed the plate, producing an image of the uranium mineral on the
developed plate. He deduced that uranium was emitting an invisible but penetrating
“radiation.” In 1898, Pierre and Marie Curie, working in the lab of Bacquerel, discovered
a property of a uranium ore, pitchblende: it could turn air into a conductor of electricity.
They called this property radioactivity, and they went on to discover two other elements
with this radioactive property, which they named polonium (after M. Curie’s native
Poland) and radium. They demonstrated that the ability of radioactive materials to
release radiation was unaffected by chemical reactions, heating the element in an electric
arc, or cooling the element in liquid air. Therefore, Marie Curie recognized that the
emanations from radioactive elements were properties of the atoms’ nuclei, because these
manipulations involved the electrons, but not the nucleus, of the elements.
Since the Curies, many other radioactive elements have been found. All the elements
with an atomic number greater than 83 are radioactive. Several elements have stable,
non-radioactive isotopes, but also have radioactive isotopes, while other elements are
always stable and have no naturally occurring radioactive isotopes. (Remember: an
isotope is an atom of an element that has the same number of protons and electrons, but
different numbers of neutrons; thus changing the mass number, but leaving the atomic
number, and therefore the identity of the element, the same). The nuclei of radioactive
isotopes are not as tightly bound as those of stable nuclei, so that after some time the
nucleus “decays” to a lower energy state; releasing particles in the process. This achieves
a higher level of nuclear stability in the remaining nucleus. This process is called
radioactive decay.
There are 3 types of particles that may be released from the nucleus in order for it to
achieve greater stability. These are alpha, beta, and gamma rays. Alpha rays (or
particles) are two protons and two neutrons, also known as the nucleus of a helium atom
( 42 He ). When a radioactive element releases an alpha particle, it loses 4 nucleons
(protons or neutrons), changing the mass number by 4, and changing the atomic number
by 2. Beta particles are high-energy electrons. Note that these are not electrons from the
outer shells of the atom, but electrons released by the nucleus. Therefore, in beta decay, a
neutron in the atomic nucleus releases a high-energy electron thereby converting the
neutron into a proton. Since no nucleons are lost in beta decay, the mass number remains
the same, but one proton is gained, so the atomic number is increased by one. Gamma
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rays are high-energy photons released from the nucleus. They put the nucleus in a lower
energy state, but they leave the number of nucleons unchanged.
Discussion question A: Complete the following radioactive nuclear reactions and define
the type of radioactive particle being emitted.
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14
6
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214
84
C147 N  __
Po  __  42 He
The rate of radioactive decay is characterized by the radioactive half-life (t1/2). This is
the time is takes for half of the radioactive sample to decay. However, the decay of any
one nucleus is a random event that follows the rules of quantum mechanics. One cannot
predict that any one nucleus will decay at any specific time, but when there is a large
enough sample, statistics predict that half of the sample will decay during the half-life.
This may seem like an arbitrary distinction, but let’s think about it with another example,
which we will see today in the lab. If you toss a coin one time, you cannot say with any
certainty that the coin will land heads-up or tails-up. However, if you toss the coin 100
times, you can approximate that 50 of those tosses will land heads-up. The random
unpredictability of any one toss, or any one decay, can be overcome by the predictability
of a large statistical sampling. Observing and timing the decay of a radioactive sample
can determine the half-life of an isotope. In today’s lab, we will calculate the half-life of
an unstable isotope of barium as it is converted into a stable barium nucleus.
Radioactive half-lives are very useful for determining the age of materials. If a sample of
unknown age contains a radioactive isotope, this parent material will decay into another
element, the daughter material. The ratio of the parent material to the daughter material
can be examined to determine how many half-lives have passed. This of course assumes
that the original sample contained negligible amounts of the daughter material, but this is
often the case. For example, Thorium 232 ( 23290Th ) decays into Lead 208 ( 208
82 Pb ) with a
half-life of 14.1 billion years. After one half-life, half of an original sample of thorium
would remain and the other half would have decayed into lead. After another half-life ¼
of the original thorium sample would remain and ¾ would be lead. Thus the ratio of
Th:Pb after two half-lives is 1:3. If you find a rock that contains 1 part thorium for every
3 parts lead (i.e. ¼ of the remaining atoms are thorium atoms), this would mean that this
rock was 2 half-lives old, or 28.2 billion years old (this is much older than the universe,
so this is only a hypothetical case).
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
Procedure
Activity 1: Radioactive simulations
In the first part of today’s lab, we will simulate the random and unpredictable nature of
radioactive decay by using a simple experiment. Record all of your data and hand in
answers to all of the numbered questions.
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Place 100 pennies in a box, and orient them all so that they are heads-up.
Have your partner time you as you shake the box for 15 seconds.
After shaking, open the box and remove all the pennies that are now tails-up.
Count the number of pennies removed and record this on your data sheet under
trial one. Also record the number of pennies remaining in the box.
Repeat this until there are no pennies left in the box, each trial removing the tailsup pennies and counting and recording the number removed as well as the number
remaining.
Data Analysis:
1. Plot a graph of pennies remaining (y-axis) vs. trial number (x-axis), beginning
with trial 0 where all 100 pennies are in the box. Fit a best-fit line to your points.
2. Does your graph demonstrate a straight-line relationship? Why or why not?
3. If the chance of any one penny ending up tails-up is random, why would you see a
predictable relationship on your graph?
4. If you say that each trial took 15 seconds, what would be the half-life of heads-up
pennies? (Your answer should be a time)
5. Describe how this experiment relates to what occurs during radioactive decay.
Activity 2: Determining the half-life of Barium 137m
Cesium 137 ( 137
55 Cs ) has a half-life of 30.17 years and it decays by beta decay into a
radioactive isotope of barium called barium 137m ( 13756m Ba ). The m denotes that the
barium is in the metastable, or excited state. In a very short half-life, the barium nucleus
will decay into the stable barium 137 nucleus ( 137
56 Ba ).
Discussion question B: What kind of decay does barium 137m undergo to form the
stable nucleus barium 137 (hint: do the mass or atomic numbers change)?
You will use a cesium/barium mini-generator (figure 1), which contains cesium 137, as
well as barium 137m, and the stable daughter product barium 137, which have been
produced by radioactive decay. The barium 137m can be washed out of the
minigenerator using a few drops of hydrochloric acid solution, while keeping the cesium
contained within the minigenerator. The half-life of barium 137m is short enough that it
can be observed in the lab. In today’s lab, you will use a Geiger counter to observe the
decay of barium 137m into barium 137 and you will time the decay in order to determine
the radioactive half-life of barium 137m.
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AP Chemistry
Figure 1: Configuration of the Cs/Ba mini-generator
and diagram of the Geiger counter.
CAUTION: This lab uses acid solutions that can burn you. Be sure to goggles
throughout this portion of the laboratory. When you wash the barium 137m out of
the minigenerator, you will have a radioactive solution in your vial. Be careful to
not spill or touch this solution, and if it is spilled, notify your lab instructor, who will
clean it up carefully. The Geiger counter is a sensitive piece of equipment; please do
not touch the face of the sensor. Be sure to wash your hands before leaving the lab
today. Read all of the following instructions before continuing.
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Turn on the Geiger counter and allow it to warm up for about 5 minutes.
When you turned on the Geiger counter, you should have noticed that it makes
random clicks. This is the background radiation, which is produced by cosmic
rays and the natural radiation in the objects around you. You can record the level
of background radiation by counting the number of clicks on the Geiger counter.
Do this setting the timer switch to 60 seconds. The counter will count the
radiation level for 60 seconds at the end of which time, the green “read display”
light will illuminate. The counter will pause for 3 seconds, and you can record
this number, and then it will clear and begin counting for a new 60 seconds.
Repeat this measurement at least 5 times so that you can get a useful average level
of the background radiation per minute. You will subtract this number from all of
your subsequent measurements of radiation. Record this on your data sheets.
Now fill your syringe with eluting solution. Remove the stoppers on either end of
the minigenerator column.
Hold the minigenerator carefully above the glass vial with the arrows on the
minigenerator pointing downward. While your partner holds the glass vial, insert
the syringe firmly into the hole on the top of the generator without pushing on the
syringe plunger.
While carefully holding the mini-generator and the vial, use the syringe to force
about 7 drops of solution into the minigenerator. DO NOT SUCK UP ON THE
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AP Chemistry

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SYRINGE; ONLY INSERT SOLUTION IN THE DIRECTION OF THE
ARROWS ON THE MINIGENERATOR. This will release the barium 137m
into the glass vial. Once you’ve pushed the solution through, remove the syringe
and place it and the minigenerator carefully back on the table.
Place the sensor window of the Geiger counter directly next to the glass vial and
you will hear an increase in the level of radiation, this is the radioactive decay of
barium 137m into barium 137.
Wait for the Geiger counter to read/display a number and then clear, so you know
you are counting a full 60 seconds before you begin recording your data. Once it
clears, it will count the level of radiation for the next 60 seconds. At the end of 60
seconds the counter will pause for 3 seconds and you can record the level of
radioactive decay per minute. After the pause, it will clear and begin to count
again.
After 3 seconds passes, repeat your measurements for another minute and record
your counts.
Repeat this at least 8 times and record all of your data on your table.
Turn the Geiger counter off and place the cover on the glass vial with the solution
in it. Replace the stoppers on the two ends of the minigenerator and return any
remaining eluting solution from your syringe into the bottle from which you
removed it.
Data Analysis:
6. Subtract the mean background counts from each of your measurements and
determine the activity A in counts/min. Plot A versus time, starting from 0
minutes.
7. Draw a smooth curve through the data points on your graph. Does the curve
approximate an exponential decay? Estimate the half-life t1/2 of the isotope (i.e.,
the time at which the activity falls to half its initial value). Does the activity fall
to 1/4 its initial value after two half-lives? To 1/8 its initial value after three halflives?
8. Measure the half-life using a curve-fitting method.
a. Mathematically, we expect the activity to depend exponentially on time: A
= Ao e(-lambda t) where lambda is the decay constant, related to the half-life
by t1/2 = 0.693 / lambda. Thus, a graph of ln A vs t should be a straight line
with slope (-lambda).
b. Enter your data into Excel and graph ln A vs t. Use Excel's LINEST
function to determine lambda from the slope of your graph.
c. What is the value of t1/2 using this method, and how does it compare with
your estimate of t1/2 from above?
9. Does the half-life of barium 137m change over time? Why or why not?
10. Given the actual half-life of barium 137m as 2.551 minutes, calculate the percent
error between the actual value and your average observed value. Use the formula:
%error  ( Observed - Actual / Actual) 100%
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Conclusions:
1. If you were given a sample of unknown age that contained 100g of
137
55
Cs and
137
700g of 137
56 Ba and you were told that it originally contained only 55 Cs , how old
would you expect the sample to be? (Hint: make sure that you consider all of the
half-lives involved in this decay!)
2. If you were told that these Cs/Ba minigenerators were purchased 5 years ago,
what fraction of the original 137
55 Cs has decayed?
206
3. If the uranium isotope 238
92 U can turn into the lead isotope 82 Pb by radioactive
decay, why were the ancient alchemists unsuccessful in using chemistry to turn
lead into gold?
4. If barium 137m has a predictable half-life that you can measure, how is
radioactive decay considered probabilistic (i.e. how are the atoms behaving like
the pennies)
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AP Chemistry
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