Hot Dice Labettini
PURPOSES:
•To illustrate the random nature of
radioactive decay
•To define radioactive “half-life”
•To demonstrate that less stable elements
decay faster and have shorter half-lives
MATERIALS (per team — 12 teams REQUIRED):
•32 dice
•Tray
Hot Dice Labettini
INTRODUCTION:
•A radioactive atom can change into another element. It
“decays” by spitting out a bit of its nucleus.
Example: 210Po  206Pb + alpha
•A radioactive atom has a certain probability of decaying
within a certain time.
Example: Any atom of 210Po has a 50% chance of decaying
in the next 138 days
•That probability never changes. Even if a 210Po atom has
already survived a gazillion years, it still has just a 50%
chance of decaying in the next 138 days.
•The time it takes for half of the atoms of a radioactive
element to decay is called the “half life”. Duh.
Hot Dice Labettini
We will simulate radioactive decay using dice instead of
atoms. We’ll pretend that one of our atomic dice decays if
it shows a certain number.
EXAMPLE:
•An “atom” decays if it’s an even number.
•So, on any given roll, the “atom” has a 50% chance of
decaying. Even if that atom comes up odd a gazillion times
in a row, it still only has a 50-50 chance of being even (and
decaying) on the next roll.
•Put another way, if we roll a bunch of “atoms”, we expect
about half to decay and half to survive.
•Put yet another way, those “atoms” have a half life of “one
roll”
Hot Dice Labettini
We will simulate radioactive decay using dice instead of
atoms. We’ll pretend that one of our atomic dice decays if
it shows a certain number.
EXAMPLE:
•An “atom” decays if it’s an even number.
•So, on any given roll, the “atom” has a 50% chance of
decaying. Even if that atom comes up odd a gazillion times
in a row, it still only has a 50-50 chance of being even (and
decaying) on the next roll.
•Put another way, if we roll a bunch of “atoms”, we expect
about half to decay and half to survive.
•Put yet another way, those “atoms” have a half life of “one
roll”
Hot Dice Labettini
SIMULATION 1: LESS STABLE ELEMENT
To simulate an unstable element that decays quickly, we’ll
pretend that an “atom” decays if it’s even after a roll. If it’s
odd, it will survive for another roll. So, half of the “atoms”
should decay after each roll, and half should survive.
• Each group will start with
32 “atoms” and roll them.
• After the first roll, remove
the “atoms” that are even.
• Record how many remain
for your group and for the
class as a whole.
• Roll the remaining “atoms”.
• Repeat for six rolls, or until
all “atoms” have decayed.
Roll
Remaining Atoms
Predicted
Yours
Class
0
384
32
384
1
192
2
96
3
48
4
24
5
12
6
6
Hot Dice Labettini
SIMULATION 2: MORE STABLE ELEMENT
To simulate a more stable element, we’ll pretend that an
“atom” decays if it equals 1 after a roll. So, 1/6 of the
“atoms” should decay after each roll, and 5/6 should
survive. (These fractions are not forbidden!)
• Each group will start with
32 “atoms” and roll them.
• After the first roll, remove
the “atoms” that are 1’s.
• Record how many remain
for your group and for the
class.
• Roll the remaining “atoms”.
• Repeat for 15 rolls or until
all “atoms” have decayed.
Roll
Remaining Atoms
Predicted
Yours
0
384
32
1
320
2
266.7
3
222.2
4
185.2
…
…
15
25.0
Class
384
Hot Dice Labettini
ANALYSIS:
•Use the graphs to estimate
the half-life of each element
in years. Remember, the
half-life is the time it takes
for half of the atoms to
decay! Record your
estimates.
300
Number Remaining
•Plot the class data for both
radioactive elements, but
pretend that each roll
represents 1 year.
400
GRAPH:
15 squares wide
20 squares high
200
100
0
0
5
10
Time (years)
15
Hot Dice Labettini
QUESTIONS:
200
400
2.What are the odds that it will be
“even” if you roll it now?
3.Will the odds of rolling “even” ever
change — no matter how many
times you roll that die?
Likewise, the half-life of an atom never
changes. No matter how long it has
survived, it still has the same chance of
making it through another day as any
other atom of the same element.
Half gone,
half left
300
150
Number Remaining
1.Pick up one die. How many times
in the life of the Universe has that
die been rolled?
200
100
100
50
0
0
Unstable half-life
5
10
Time (years)
Stable half-life
15
Hot Dice Labettini
SUMMARY:
•Radioactive decay is RANDOM and does
NOT depend on history!
•Half of the atoms of a radioactive element
will decay within a half life.
•Less stable elements have shorter half
lives.