Half-life Simulation Lab for Nuclear Decay
The half-life of a radioactive nuclide is length of time during which half of a given
number of atoms of the element will decay. In a given sample population of unstable
atomic nuclei, within one half life each nucleus has fifty percent chance of decaying.
Thus, after one half life approximately 50% will have decayed. After another half life,
50% of the remaining nuclei will decay; after a third half life 50% of those that remain
will decay, and so on.
This penny tossing experiment simulates radioactive decay. When a penny is tossed,
it has 50% chance of being a head or a tail. We can take heads as decayed and tails as
non-decayed nuclei. This will simulate only number of half lives. This data will not be
used to determine half life.
Procedure:
1. Toss 40 pennies.
2. Remove and count the number of heads (Nh). Record the number of heads in Table 1.
This represents the number of nuclei that have decayed in one half life. Count the number
of tails (Nt) and record them as nuclei that did not decay in this half life.
3. Calculate percentage of decayed nuclei using number of heads divided by number
of pennies tossed and multiply by 100.
4. Toss the remaining tail pennies. Repeat steps 2 and 3.
5. Keep repeating and recording until all pennies are heads. Record every toss, even
if no pennies land as head. That only represents a situation when no nucleus decayed.
6. Repeat steps 1 – 5 two more times recording data in Tables 2 and 3.
7. Transfer values from the three tables to Table 4 in the appropriate columns. Get
average of all the tails (Nt), non-decayed nuclei and record it as Nt Average.
8. Record natural log of Nt Average in Table 4.
9. Graph Nt Average versus number of half lives.
10. Graph natural log values of Nt average versus number of half lives.
Table 1
__________________________________
Number
Nh
Nt
% decayed
of half
(heads)
(tails)
lives
decayed non-decayed
__________________________________
0
___________________________________
1
__________________________________
2
__________________________________
3
__________________________________
4
__________________________________
5
__________________________________
6
__________________________________
7
__________________________________
8
_________________________________
9
_________________________________
10
_________________________________
Table 2
_________________________________
Number Nh
Nt
% decayed
of half (heads) (tails)
lives
decayed non-decayed
_________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
Table 3
__________________________________
Number
Nh
Nt
% decayed
of half
(heads) (tails)
lives
decayed non-decayed
__________________________________
0
__________________________________
1
__________________________________
2
__________________________________
3
__________________________________
4
__________________________________
5
__________________________________
6
__________________________________
7
__________________________________
8
__________________________________
9
__________________________________
10
__________________________________
Table 4
__________________________________
Number Trial 1 Trial 2 Trial 3 Nt Ln
of half
Ave Nt
lives
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
_________________________________