Radioactivity and Half-Life Exercise
Elements are made of 3 major sub-atomic particles called protons, neutrons, and electrons. The
number of protons in an atom are what defines the element. Hydrogen always has 1 proton and oxygen
always has 8 protons, for example. Most elements on the periodic table have been known for many
years, but some of the largest elements have only recently been discovered. The last 4 elements missing
from the periodic table were just officially discovered by groups of scientists from the United States,
Russia, and Japan. They are have atomic numbers of 113, 115, 117, and 118. They are outlined in orange
in the last row of the periodic table below.
http://newshour-tc.pbs.org/newshour/wp-content/uploads/2016/01/periodic-table_wikimedia-Diep-1024x561.png
Part of why these elements are so hard to discover is because they are radioactive, or highly
unstable. This means that these elements break down or decay into other elements. Some radioactive
elements decay slowly over millions of years. Others, like these new elements decay very fast. The rate
radioactive elements decay is called a half-life.
To understand half-lives, let’s use M&M’s. Your blue M&M’s are stable and NOT radioactive.
Your red M&M’s are radioactive. Let’s start with 16 red M&M’s.
Every 60 seconds, your teacher will say “Decay!” and you will replace exactly ½ your red M&M’s
with blue ones. The half-life of the red M&M’s in this case is 1 minute. Every minute, you will only have
half as many red M&M’s as before.
Step 1: Separate 16 red and 16 blue M&M’s and put the blue ones aside. Your teacher will say “Start”.
Start:
0 seconds
Reds:
16
Blues:
0
Step 2: Your teacher will say “Decay!” Now you should discard (or eat) exactly half of your red M&M’s.
Replace the missing red M&M’s with blue ones. How many of each do you have now?
1 half-life:
1 minute
Reds:
8
Blues:
8
Step 3: Your teacher will say “Decay” again. You should remove half of your remaining red M&M’s and
replace them with blue ones again. How many reds and blues do you have now? (Hint: The total
number of M&M’s should always equal 16.)
2 half-lives:
2
Reds:
4
Blues:
12
3
Reds:
2
Blues:
14
4
Reds:
1
Blues:
15
Step 4: Decay again.
3 half-lives:
Step 5: Decay again.
4 half-lives:
Q: If there was another step, how many red M&M’s would you expect to have?
Either 1 or 0 is acceptable because it is impossible to have ½ an atom.
Q: Now think about some of the new elements. The scientist were only able to make 8 atoms of element
115 and it has a half-life of only 20 milliseconds! Using your M&M data, how many half-lives
would it take for all the atoms the scientists created to decay away?
After 4 half-lives, no atoms of 115 should remain.
Q: How long did element 115 exist? (Hint: Multiply the number of half-lives from your previous answer
by 20 milliseconds.)
80 milliseconds or 0.08 seconds!
BONUS (optional):
You can also have your students plot the data with time on the x-axis and the # of M&M’s on the y-axis.
The red and blue M&M curves should be exponential curves that are mirror images of each other:
Radioactive Decay of Red M&M's
16
15
14
13
12
11
# of M&M's
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
Time (Minutes)
Red M&M's
A blank graph is attached below for students.
Blue M&M's
4
5
Radioactive Decay of Red M&M's
16
15
14
13
12
11
# of M&M's
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
Time (Minutes)
Red M&M's
Blue M&M's
4
5