(has to do with the nucleus, get it?!)
Take Home Unit Packet!
(you’ll get this joke better once you read the next page….)
I) Intro
In 1896 French chemist Antoine Becquerel accidentally discovered that
uranium emits invisible rays. Marie and Pierre Curie were his students and they
showed that film could be “fogged” or exposed by the rays given off by uranium
ore. This radiation was a result of….
II) Radioactive Decay (Radioactivity)
A) What is it? The spontaneous breakdown of an atom’s nucleus.
In a chemical reaction the nucleus never changes, only electrons are
transferred or shared. In a nuclear reaction the nucleus always changes,
thus changing the identity of the atom.
B) Why does it occur? The nucleus may be unstable based on the
neutron-to-proton ratio. It will then spontaneously break down
until it attains a more stable neutron-to-proton ratio.
Check out the graph on the following page which shows the number of
neutrons in the atom as it relates to the number of protons in an atom.
The belt of stability represents a neutron-to-proton ratio which is stable,
resulting in nuclei that do NOT decay. Anything outside of the belt of
stability has a neutron-to-proton ration which is unstable, resulting in
nuclei that do decay.
C) What does it result in? The decay process results in the release
of energy (radiation) and particles. A new element is also formed
as the nucleus breaks down and changes its composition.
Because the nucleus changes, the identity of the element also changes.
This is why a new element can be formed in a nuclear reaction, but not a
chemical reaction.
D) Which elements are naturally radioactive? Technetium (atomic
number= 43), Polonium (atomic number= 84) and any element
higher are always radioactive. Sometimes an element which is
normally stable has a certain isotope that is radioactive called a
radioisotope. Many times these radioisotopes are high neutron
isotopes (ex. C-12 is not radioactive, C-14 is radioactive).
Most elements are NOT radioactive and do NOT decay. Still, many
elements do have a rare isotope that is radioactive. Elements 84 and
above are always radioactive, no matter what the isotope is.
E) What is natural transmutation? The spontaneous changing from
one element to another.
This is really is the same thing as radioactive decay but with a new focus.
Natural means that it happens in nature without any outside intervention.
The word transmutation specifically describes the formation of a new
element. This is exactly what happens during radioactive decay, the
formation of a new element.
F) What factors do NOT affect radioactive decay? Unlike chemical
reactions, temperature, pressure, concentration, surface area,
and catalysts do NOT affect the decay rate.
The decay is determined only by the stability of the specific nucleus and is
thus not affected by outside forces. Therein lies one of the problems of
radioactivity, it can’t be speeded up or slowed down! It does what it does
and there’s nothing you can do about it!
Number of Neutrons vs. Number of Protons in an Atom
Radioactive Decay Worksheet
1. Define radioactivity.
2. How are chemical and nuclear reactions different from one another?
3. Why do nuclei spontaneously decay?
4. What is the belt of stability?
5. An element has 50 protons and 90 neutrons. Will the nucleus breakdown?
Why or why not?
6. Will a nucleus of Zn-65 be stable or unstable? Explain. (Hint: the 65
represents the mass number of zinc)
7. What are the products of radioactive decay?
8. List elements which are always radioactive.
9. What is a radioisotope?
10. Define natural transmutation.
11. How would an increase in temperature affect the rate of radioactive decay?
III) Types of Radioactive Decay
Please note Table O as you read about each decay mode. Note: protons and
neutrons are of interest in this unit, but they are NOT types of radioactive decay.
A) Alpha Decay ()
An alpha particle is released from the nucleus as it decays. An
alpha particle is the same thing as a helium nucleus and is often
given the notation He. Alpha particles have a mass of 4 (the top
number) and a charge of +2 (the bottom number).
Alpha particles are very large and move very slowly. They are not
considered to be dangerous when they are emitted from an atom’s
nucleus because they cannot pass through even a piece of paper let alone
a person’s skin. We say that alpha particles have a low penetrating
power. It can, however, cause matter around it to ionize, so it is
considered to have a high ionizing ability.
B) Beta Decay (-)
A beta particle is released from the nucleus as it decays. A beta
particle is the same thing as an electron and is often given the
notation -1e. A beta particle has a mass of 0 (the top number)
and a charge of –1 (the bottom number).
You may wonder how an electron can be emitted from an atom’s nucleus.
In fact, a neutron breaks down into an extra proton which remains in the
nucleus and an electron which is given off. Beta particles are of medium
size and move at a medium speed. Beta particles are slightly more
dangerous than alpha particles, but they can be stopped by something
thicker than paper such as metal foil. We say that beta particles have a
medium penetrating power. It can cause matter around it to ionize, so it
is considered to have a medium ionizing ability.
C) Gamma Radiation ()
Unlike alpha and beta particles, gamma radiation is not a particle
released from the nucleus as it decays. Instead, it is a form of
electromagnetic radiation. It has a mass of 0 (the top number)
and a charge of 0 (the bottom number).
Almost all radioactive decay modes are accompanied by the release of
gamma radiation. Gamma radiation moves at the speed of light, so it is
very fast. Gamma radiation is very dangerous, since it can only be
stopped by lead or concrete. We say that gamma radiation has a very
high penetrating power. This is the cause of radiation sickness associated
with radioactive waste spills or atomic bomb fall out. It does not cause
matter around it to ionize, so it has almost no ionizing ability.
Highly recommended: check out the following web link for a nice review
with good visuals. Try out the practice quiz for extra practice.
http://www.darvill.clara.net/nucrad/types.htm
Note: the last form of decay is still very important, it’s just that most
textbooks and websites don’t list it under the 3 main types of decay. Oh
well, we’ll still learn about it!
D) Positron Decay (+)
A positron particle is released from the nucleus as it decays. A
positron particle is the same thing as a positively charged
electron and is often given the notation +1e. A positron has a
mass of 0 (the top number) and a charge of +1 (the bottom
number).
You may wonder how a positively-charge electron is produced. In fact, a
proton breaks down into an extra neutron which remains in the nucleus
and positron which is given off.
Decay Mode Worksheet
1. List the four types of radioactive decay.
2. Use Table O to write the correct notation for an alpha particle. Describe what
each number in the notation means.
3. Why is the emission of an alpha particle not particularly dangerous to people?
4. How is a beta particle produced by a nucleus?
5. Describe the speed and penetrating power of a beta particle.
6. What can stop a beta particle from passing?
7. How is gamma radiation different from the other forms of decay?
8. Why is gamma radiation so dangerous to people?
9. What is a positron? How is it produced?
10. What subatomic particle listed on Table O has the same charge as gamma
radiation?
11. Name all subatomic particles listed on Table O that would be affected by a
magnet.
IV) Radioactive Decay Equations
A radioactive decay equation should always have one reactant (the
element decaying), a particle emitted as a product (based on the decay
mode) and the new element created as a product. The new element is
determined by making sure the masses (top number) on both sides of
the equation are equal and the charges (bottom number) on both sides
of the equation are equal. The bottom number is also the atomic
number and ultimately determines the identity of the new element.
Given a radioisotope, you can look on Table N to find out its decay mode. We
will discuss half-life later in this unit.
Rules for Equation Writing
1. You will be given a radioisotope
(also known as a nuclide). Since
it decays on its own, write it
down as the only reactant. You
may have to determine the
atomic number off of the
Periodic Table. Add an arrow.
2. Using Table N, determine the
decay mode.
3. Using Table O, determine the
full notation of the emitted
decay particle from Table N.
4. Write this notation for the
particle to the right of the arrow
as a product.
5. The top numbers (mass) on
each side of the equation must
be equal on both sides.
Determine the top number of
the new element.
6. The bottom numbers (nuclear
charge) must be equal on both
sides. Determine the bottom
number of the new element.
7. Using the lower number (atomic
number) and your Periodic
Table, write the symbol of the
new element.
Examples: Read through the
examples step by step so that you
fully understand how to write
radioactive decay equations.
Writing Decay Equations Worksheet
1. Compare the decay modes of K-37 and K-42, according to Table N.
2. Write the decay equation for K-37.
3. Write the decay equation for K-42.
4. Which of the following would be more dangerous, radon-222 or cobalt-60 in
the same dosage? Explain.
5. Write the decay equation for radon-222.
6. Write the decay equation for cobalt-60.
V) Half-life
A) What is it?
The amount of time it takes for half of a sample’s nuclei to decay.
The amount of time for half of the sample to decay, regardless of
amount, remains CONSTANT.
It is important that you realize that half of the nucleus doesn’t decay, but
half of the atoms in a given sample decay during after one half-life.
B) Who cares?
What’s interesting about half-life is that no matter how many
atoms you start with, half of them will decay after one half-life.
After a second half-life, half of the atoms that remain after the
first decay, decay themselves. After a third half-life half of the
atoms that remain after the second decay, decay themselves and
so on. Note: the time that passes after each half-life does NOT
change! (see the graph below)
Although from a mathematical standpoint you wouldn’t expect to ever
reach zero where all atoms are decayed, in reality, eventually all atoms
will decay and you WILL reach zero.
C) How do I know what a radioisotopes’ half-life is?
Use Table N to look up the half-life for each nuclide.
Each radioisotope has its own distinct half-life that cannot be changed.
Changes in temperature, pressure, concentration, surface area, and
catalysts do NOT affect the decay rate and thus do NOT affect the halflife.
D) What does the value for half-life tell me?
Each radioisotope has its own distinct half-life value which tells
you how long it takes for half of the sample to decay.
Radioisotopes with short half-lives are less dangerous because they decay
more quickly. Radioisotopes with long half-lives are more dangerous
because they decay slowly and thus, stay radioactive longer. This is a
particular problem with radioactive waste.
Highly recommended: check out the following web link for a nice review
with good visuals. Try out the practice quiz for extra practice.
http://www.darvill.clara.net/nucrad/hlife.htm
Half-life Concepts Worksheet
1. What is half-life?
2. After three half-lives, what fraction of the original sample would remain?
Explain.
3. A 50 gram sample of a radioisotope undergoes 2 half-lives. How many grams
would remain at the end? Explain.
4. Name the element on Table N that has the shortest half-life that undergoes
alpha decay.
5. Would the nuclide from #3 be dangerous to living things based on its halflife? Why or why not?
6. Which radioisotope on Table N has the longest half-life?
7. Would the nuclide from #5 be dangerous to living things based on its halflife? Why or why not?
8. A radioactive sample of C-14 is heated. How is the half-life affected?
VI) Half-life Calculations
Check out the following example problems shown below. Use them as models
for the worksheet that follows.
Ex 1) How many grams remain of a 10.0 gram sample of cobalt-60 after 15.78
years?
Step 1: Determine the half-life from Table N: 5.26 years
Step 2: Calculate the number of half-lives that have passed:
# of half-lives = total time/1 half-life = 15.78 y/5.26 y = 3 half-lives
Step 3: Set up a chart that shows the amount decaying by ½ with the
passing of each half-life. Hint: Make sure that the initial amount is
always before the first half-life at 0.
# of half-lives
0
1
2
3
Fraction remaining
1
1/2
1/4
1/8
Grams remaining
10.0 g
5.00 g
2.50 g
1.25 g
Step 4: State the final answer: After 15.78 years (3 half-lives), 1.25 grams of
cobalt-60 remain.
Ex 2) What mass of iodine-131 remains 32 days after a 100. g sample of the
isotope is obtained.
Step 1: Determine the half-life from Table N: 8.07 days
Step 2: Calculate the number of half-lives that have passed:
# of half-lives = total time/1 half-life = 32 d/8.07 d = 4 half-lives
Step 3: Set up a chart that shows the amount decaying by ½ with the
passing of each half-life. Hint: Make sure that the initial amount is
always before the first half-life at 0.
# of half-lives
0
1
2
3
4
Fraction remaining
1
1/2
1/4
1/8
1/16
Grams remaining
100. g
50.0 g
25.0 g
12.5 g
6.25 g
Step 4: State the final answer: After 32 days (4 half-lives), 6.25 grams of
iodine-131 remain.
Ex 3) A sample of an isotope decays from 100. grams to 25.0 grams in 20 days.
What is the half-life of the unknown radioisotope?
Step 1: Determine the number of half-lives with a chart showing the
decay of the original amount to the final amount:
# of half-lives
0
1
2
Fraction remaining
1
1/2
1/4
Grams remaining
100. g
50.0 g
25.0 g
Thus, 2 half-lives have occurred.
Step 2: Divide the total time by the number of half-lives to obtain the
half-life: half-life = total time/# of half-lives = 20 d/2 half-lives = 10 days
Step 3: State the final answer: The half-life (time for half to decay) is 10
days.
Ex 4) If a sample of Sr-90 has a mass of 100. grams, how long will it take to
decay such that only 12.5 grams of Sr-90 remains?
Step 1: Determine the half-life from Table N: 28.1 years
Step 2: Determine the number of half-lives with a chart showing the
decay of the original amount to the final amount:
# of half-lives
0
1
2
3
Fraction remaining
1
1/2
1/4
1/8
Grams remaining
100. g
50.0 g
25.0 g
12.5 g
Thus, 3 half-lives have occurred.
Step 3: Determine the total time by multiplying the half-life by the
number of half-lives: 28.1 y x 3 = 84.3 y
State 4: State the final answer: It takes 84.3 years for Sr-90 to decay from
100. grams to 12.5 grams.
Half-life Calculations
1. How much of a 100. gram sample of
198Au
is left after 8.10 days?
2. A 50.0 gram sample decays to 12.5 grams in 14.4 seconds. What is its halflife?
3. How much of a 750.00 gram sample of K-42 is left after 62.00 hours?
4. What is the half-life of an element if a 500. gram sample decays to 62.5
grams in 639,000 years?
5. If there are 25.0 grams of a sample of thorium-232 left after 2.80 x 1010
years, how many grams were in the original sample?
6. How long will it take for 16 grams of Ra-226 to break down until only 1.0
grams remain?