When a radioactive sample decays, there is one less parent nuclei and one more daughter nuclei. As this decay process continues, the number parent nuclei decreases and the number of daughter nuclei increases. Eventually there are no parent nuclei increases. Eventually there are no parent nuclei left to decay into daughter nuclei and no further decays occur.
In this activity, you will use a model to see how the rate of radioactivity of a sample changes over time. In this investigation, you will use popcorn kernels to represent parent nuclei.
QUESTION:
What happens to the rate of radioactive decay in a sample as time passes?
PREDICTION:
I think that the rate of decay increases.
MATERIALS: - 100 popcorn kernals
- petri dish
PROCEDURE:
1. Copy table 1 into your notebook. You will begin with 100 popcorn kernels. Since these represent parent nuclei, they will be referred to as parent kernels. The first row in the table shows that there are 100 parent kernels and no daughter kernels.
2. Count the popcorn kernels to make sure that there are exactly 100. Put the kernels in a container, shake the container, and carefully drop the kernels on your desk. Imagine each kernel as the hour hand of a clock. If the point of the kernel is between 12 and 3 on the "clock", assume that the kernel has decayed. Fig 1 shows how to determine which kernels have decayed and which are still alive. Decayed kernels represent daughter nuclei. Count the number of daughter kernels and record the number in your table. Record in ur table how many parent kernels are left. this is one unit of time as measured in shakes.
3. Remove the daugter kernals. Put the parent kernels back in the container and repeat step 2. This is the second unit of shake time.
4. Repeat step 3 until all of the parent kernels have decayed and there are no parent kernels left. Always record the number of decayed popcorn-even if # is zero.
5. Make 2 graphs. On 1st graph, plot the # of daughter kernels produced versus time as measured in shakes. On the 2nd graph, plot the # of parent kernels remaining versus time as measured in shakes. Draw a line of best fit for each graph. In this case, the line should be curved.
My results:
Time shakes = Ts
Parent kernels = Pk
Daughter kernels = Dk
Ts | Pk | Dk
0 100 0
1 72 28
2 58 42
3 36 64
4 20 80
5 15 85
6 8 92
7 4 96
8 2 98
9 0 100
I have a few questions which I got stumped on.
1. On the graph of parent kernels versus time, at what time (as measured in shakes) did the number of parent kernels become approximately 50? How much more time passes before the number of parent kernels was reduced to approximately 25? How do these two numbers compare?
Answer~
The number of parent kernels became approximatley 50 at the second unit of shake time. Two units of shake time passed before the number of parent kernels was reduced to approximately 25. How do these two numbers compare though?
2. Using your response to (d), what is the half life of popcorn as determined by ur results?
~Can't seem to figure it out. I think the formula is total time over half life. The total time would be I think 9, but what would the half life be?
Thanks for all ur help
1. Did you get this off the graph? You ought to have a better number than "two units of shake time..."
Read off the graph, not the data table.
Half life is the time it takes to reduce by 1/2 the number of kernels.
1. To determine the time (as measured in shakes) when the number of parent kernels became approximately 50, you can refer to the data in Table 1, specifically the "Pk" column. From the data, you can see that at time 2 (measured in shakes), there were 58 parent kernels remaining. Since this value is closest to 50, the approximate time when the number of parent kernels became 50 is 2 units of shake time.
To find out how much more time passes before the number of parent kernels was reduced to approximately 25, you can look for the time when the number of parent kernels in the "Pk" column becomes closest to 25. From the data, at time 5, there were 15 parent kernels remaining. Therefore, it took 3 more units of shake time for the number of parent kernels to reach approximately 25.
To compare these two numbers, you can subtract the time when the number of parent kernels became 50 (2 units) from the time it took to reduce the number of parent kernels to approximately 25 (3 units). So, 3 - 2 = 1. The second unit of shake time occurred 1 unit of time before the third unit of shake time.
2. To determine the half-life of popcorn as determined by your results, you need to calculate the average time it took for the number of parent kernels to reduce by half. From the data, you can see that it took 4 units of shake time for the number of parent kernels to reduce from 100 to approximately 50. Therefore, the half-life of popcorn (time taken to reduce by half) is 4 units of shake time.