You have been learning about radioactive decay of atoms and
about half-life. In this simulation you will cut a piece of
paper on a regular schedule to have a hands-on model for
the math of half-life. In the boxes below you will see the
formulas wewill be using with all variables identified.
R = (1/2)n
R is the fraction of the material that
remains after some amount of time has passed. | n
is the number of half-lives that have passed.
ttotal = nt1/2
ttotal is the total time | n is
the number of half-lives that have passed |
t1/2 is the length of the half-life
Read the directions completely before beginning. You
will be cutting a piece of paper in half once every 30
seconds for 4 ½ minutes.
You have a radioactive piece of paper. It represents a
large number of atoms that are radioactive and which decay
at a specific rate. To simulate this decay cut the piece of
paper in half. Set aside one half. This half has already
decayed and the atoms in that half are no longer
radioactive. Mark the decayed half with a numeral one. In
your data table note that it took 30 seconds to reach the
point where one half of your atoms have decayed.
After 30 more seconds cut the remaining piece of paper
in half. Mark one of the new pieces with a numeral two and
set it with the piece marked with a one. Now one quarter of
the original atoms remain radioactive and three quarters
are stable.
Wait 30 seconds and then cut your remaining piece in
half again. Mark one piece with a numeral three and set it
with the other marked pieces.
Repeat this process until you have cut the paper in
half a total of nine times. Then proceed to answer the
questions below.
Questions
Work with your group to answer the following questions but
record your own answers here. Phrase each answer in the
form of a complete sentence, where appropriate.
Fill in the following table based on the paper (sample
of atoms) you cut up.
Number on Piece (n)
Fraction of Original Atoms (R)
Percent of Original Atoms (R)
Total Time up to Cutting this Piece (ttotal)
In this simulation, what does the
whole sheet of paper represent?
What do the pieces you set aside
and marked with numbers represent?
What do the pieces you
haven’t cut yet represent?
How much paper remained un-cut
after 1.5 minutes?
How much paper remained un-cut
after 4 minutes?
Will there ever be a time when the
paper is too small to cut anymore? What does this fact
represent in terms of radioactive atoms?
What is the half-life, in seconds,
for the paper-cutting in this simulation?
What is the relationship between
the number on the piece of paper and how many half-lives
have passed?
Write a short summary of how this
simulation worked to communicate how radioactive decay
works and how it can be described by half-life. Use the
terms “fraction remaining”,
“half-life”, “number of
half-lives”, and “total time” in your
description. Be specific and use numbers when possible.
What fraction of the paper would
remain after 5.5 minutes?
If an isotope has a half-life of
20 minutes then how long will it take to decay to 12.5% of
the original amount?
If an isotope has a half-life of
20 minutes then how long will it take to decay to 6.25% of
the original amount?
If an isotope has a half-life of 10 minutes then how
long will it take to decay to 3.125% of the original
amount?
Before beginning the activity, introduce students to the
idea of decay rates by defining the key terms and showing
them the way the number of atoms that are still radioactive
changes over time using a simulation such as the Radioactive Dating Game simulation from
PhET. This activity can be done to prepare students for the
activity which provides an introduction
to half-life.
Last updated: Jan 02, 2019
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