MODELING DECAY AND HALF-LIFE

Scientists use several different methods of dating fossils. One of these is radioactive dating. Each radioactive atom can decay, giving off nuclear particles and becoming a more stable element. Although we don't know when any given atom will do this,radiometric dating depends on the fact that each radioactive element decays at a known rate. Half-life is the period of time it takes for a substance undergoing decay to decrease by half. Different radioactive isotopes have different half-lives, lasting from nanoseconds to billions of years, depending on the stability of the nucleus. By knowing the half life of an element, the amount of the radioactive element left and the amount that has decayed (the amount of the new element) we can figure out approximately how old a fossil or a sample of rock is.The table below shows the reduction of a quantity in terms of the number of half-lives elapsed.

Number of
half-lives
elapsed / Fraction
remaining / Percentage
remaining
0 / 1/1 / 100
1 / 1/2 / 50
2 / 1/4 / 25
3 / 1/8 / 12 / .5
4 / 1/16 / 6 / .25
5 / 1/32 / 3 / .125
6 / 1/64 / 1 / .563
7 / 1/128 / 0 / .781
... / ... / ...
n / 1/(2n) / 100/(2n)

Step 1. Place all pennies in a flat box (one with a cover) so that all are tails up. Cover the box and shake thoroughly.

Step 2. Remove all the pennies that are now heads up. Record this number on a chart. These represent the atoms that have decayed through one t1/2. On your chart record the number remaining in the box as well.

Step 3. Continue to follow step 2 until all the pennies are removed from the box. Make certain you record the number of trials needed to complete the process. Each trial is one shaking of the box and removal of the heads up items.

Step 4. On graph paper make the following plot: Place the number of trials (l...x) on the horizontal axis equally spaced apart. On the vertical axis place the number of pennies used (1...100) equally scaled apart. Plot the number of atoms that did not decay (remained in the box) per trial.

Step 5. Make certain your graph contains all the needed titles, axis labels, etc. (See pg 2).


Number of half-lives
(Shake #) / Number of pennies decayed / Number of pennies remaining

Graph your data on the graph paper provided on the back. Remember to include a TITLE, and LABEL the X and Y AXES. Your graph should look similar to, but not the same as, the graph below.

Science Questions

1. How many shakes did it take you to get rid of all of your pennies? How did this compare to the other groups?

2. Sodium 24 (Na 24) has a half life of 15 hours. Fill in the following table showing the decay of a 100g sample.

grams of Na -24 / hours passed
100 / 0
50 / 15
30
12.5
6.25
75

3. Using the table from question 2, if 105 hours have passed how much of the original 100 gram sample should be left?

4. Carbon 14 has a half life of 5770 years. If you start out with 100 grams of carbon 14 in how many years will you only have 25 grams left?

5. In what way is the penny toss like the decay of a radioactive element?