Using
Dice to Model the Radioactive Half-life of an Isotope
Procedures
(trial one: Oneortwoium)
In
this trial each of the dice represents one gram of the parent isotope
Oneortwoium.
Each
shaking event will represent one year of time.
Dice
that land on 1 or 2 will be represent one gram of daughter isotope.
1. Your group should have 60 dice, one of which
is a different color. Count them to make
sure
they are all there.
2. Place all of the dice in the container you
have been given and shake them up well and then
pour them out onto your lab bench.
3. Remove all the dice that land on 1, or
2. Each of these represents one gram of
daughter
isotope.
4. Count the number of dice remaining after the
first shake and record this number on your data
table in the column labeled “Grams of
Oneortwoium”. This represents the number
of grams
of remaining Oneortwoium.
5. Take the remaining dice (the ones that landed
on 3 - 6) which represent the ones that did
not decay, and return them to the
container and shake them up again.
6. Pour the dice onto your lab bench again and
repeat steps 3 – 5.
7. Continue this process for ten shakes, or
until all of the dice have “decayed”.
Procedures
(trial two: Justsixium)
In
this trial each of the dice represents one gram of the parent isotope
Justsixium.
Each
shaking event will represent one year of time.
Dice
that land on 6 will be represent one gram of daughter isotope.
8. Repeat the steps above, starting over again
with all 60 dice. This time you will
imagine that
each of the dice represents a gram of
Justsixium.
This time, instead of removing dice that
land on 1, or 2, you will only remove dice that land
on 6.
9. After each shake, count the number of dice
that have not decayed and write this on your data
table in the column labeled “Grams of
Justsixium”
10.
Continue this process for ten shakes, or until all of the dice have “decayed”
to 6.
Pay attention to when the one mismatched
dice decays. Put a box around the value
on the
data table when this one finally decayed.
Half-life
Lab Name
____________________
Data Table
Number of Years Grams of Oneortwoium Grams of Justsixium
(1
shake = 5yrs) (1 dice = 1 gram of Oneortwoium) (1 dice = 1 gram of Justsixium)
0 80 80
_____5______ ______»
50_______ _______» 65______
______10_____
_______________ _______________
_____15_____ _______________ _______________
____20_____ _______________ _______________
_____25_____ _______________ _______________
_____30_____ _______________ _______________
_____35_____ _______________ _______________
_____40_____ _______________ _______________
_____45_____ _______________ _______________
_____50_____ ______»
0______ _______»
10______
11.
Graph the data for the decay of Oneortwoium on the graph paper provided.
Draw a smooth best-fit curve through the
data and label the curve “Oneortwoium”
12. Graph the data for the decay of
Justsixium on the graph paper provided.
Draw a smooth best-fit curve through the
data and label the curve “Justsixium”.
Questions
1.
To find the half-life of each isotope, see how many years (shakes) it
took it to reduce itself
from 80g to 40g. Half-life of
Oneortwoium:_____ »
8______
Half-life
of Justsixium: _____»
17_______
2. How many more years did it take
to reduce the amount of isotope from
40g to 20g (50% to 25%)?
Oneortwoium:___ »
8___ Justsixium: ____» 17____
You should find that this is the same amount of time as one half-life.
3. Which isotope would be more radioactive? Choose
the one that decays the fastest since it gives off
more particles in a given amount of time
4. If Oneortwoium had too many neutrons to be
stable, what type of particle would it emit?
Electron emission
If Justsixium had too a large nucleus that
was too large to be stable, what type of particle
would it emit? Hint: too big = 84 or
more protons
Questions
(continued)
5. If you walked in in the middle of this lab
and found that your lab partners were part way
through “trial one: Oneortwoium” and they only had 8 of the original 80
dice left in their
box, how many shakes would you estimate
that they had completed? _________________
If each shake was equal to one year, how
many years would this be? ________________
6. About how many half-lives does it take any
parent isotope to be reduced to 3.1% of its original
amount?
________
If you had
only 3.1% of the original amount of Justsixium, how old would the sample be?
_____
(remember
that one shake = one year)
7. If you
started with 60g of Justsixium, how many grams would you expect to have left
after 15
years? ___________
If you
started with 1000g of Justsixium, how many grams would you expect to have left
after 15
years? ___________
8. If you
started with 60g of Oneortwoium, how many grams would you expect to have left
after 15
years? ___________