Name: Asif Awan

Year: 11

Teacher: Mr. Khan

Task: Lab Report

Aim: To use dice to stimulate nuclear decay and investigate the methods of finding half-life

Equipment: 40 six sided fair dice in a plastic container.

Method/Procedure:

1. Collect a container of six sided dice from your teacher2. Count how many dice you have.3. When a die rolls 6 uppermost, it is considered to have decayed.4. Throw the dice on to the desktop.5. Collect all the dice that have decayed.6. Now place all the remaining dice into the container and throw them on to the desktop.

Repeat this process until you have completed 15 throws (or less, id all dice decay before this).

7. Repeat the whole experiment at least four times and record all your data.

Observations:

Dice decay is mainly based upon probability just like a radioactive decay.

Group members weren’t shaking the dice container properly. Few sources of error were there like release of dice with very low

energy, predicting that it will show a six.

Results:

Throws

Decays(number of 6s thrown) Undecayed dice left Your results

Class results

Trial 1 Trial 2 Trial 3 Trial 4 Trial 1 Trial 2 Trial 3 Trial 4 Total Total0 0 0 0 0 40 40 40 40 40 401 5 5 8 4 35 35 32 36 35 332 4 9 5 3 31 26 27 33 29 273 5 6 6 6 26 20 21 27 24 224 2 2 6 5 24 18 15 22 20 195 2 2 0 2 22 16 15 20 18 166 3 4 1 3 19 12 14 17 16 137 1 3 2 3 18 9 12 14 13 118 5 0 3 3 13 9 9 11 11 99 3 1 2 4 10 8 7 7 8 710 2 3 4 1 8 5 3 6 6 611 1 0 2 0 7 5 1 6 5 612 0 2 0 2 7 3 1 4 4 513 1 0 0 1 6 3 1 3 3 314 2 1 0 1 4 2 1 2 2 215 1 0 0 0 3 2 1 2 2 2

Sources of Error:

While conducting the investigation, the students did not shake the dice container properly, which could have made a difference in results obtained. Students also did not release the dices from their hands when less than five dices were left and also didn’t release dice with similar action and few students released all dices very close to the surface not allowing probability reach its full potential.

Graph 1 based on group results:

Graph 2 based on class results:

Recording Results:

Half-Life for class results:

0 2 4 6 8 10 12 14 160

5

10

15

20

25

30

35

40

45

f(x) = 40 exp( − 0.191353354397481 x )

Number of throws vs Undecayed dice left (Group results)

Number of throws vs Undecayed dice leftExponential (Number of throws vs Undecayed dice left)

Throws

Unde

cayd

dice

left

(Gro

up R

esul

ts)

Initial number of Undecayed dice

Half the initial number of

Undecayed dice

Number of throws at the

initial number(from

graph)

Number of throws at half the

initial number(from

graph)

Difference(half-life)

0 2 4 6 8 10 12 14 160

5

10

15

20

25

30

35

40

45

f(x) = 40 exp( − 0.196578551005076 x )

Number of throws vs Undecayed dice left (Class results)

Number of throws vs Undecayed dice leftExponential (Number of throws vs Undecayed dice left)

Throws

Unde

cayd

dice

left

(Cla

ss R

esul

ts)

Half-life ((with reference to class results) = + + + +

Half-Life for group results:

Initial number of Undecayed dice

Half the initial number of

Undecayed dice

Number of throws at the

initial number(from

graph)

Number of throws at half the

initial number(from

graph)

Difference(half-life)

Half-life (with reference to group results) = + + + +

Extension

1) Decay is a random process controlled by probability. It follows a rule where the following equation applies:

N=N0e-kt

Does your data follow an appropriate curve to fit this model?

Yes! It does follow an appropriate curve to fit the given model.

2) N is the quantity at time t, and N0 is the starting quantity. What is the probability in this experiment, on any one throw, of any one particular die decaying?

Probability=

3) A computer based spread can fit a line-of-best-fit, or trend line, to a set of data points. Use your spreadsheet to insert a trend line and ask for an exponential line to be fitted with the equation of the line displayed. What is the “k” value of the exponential trend line fitted to your data?

4) Mathematically, t1/2= 0.693. Use your k value from question 3 in this formula to find the half-life. How does this value compare to the average value found directly from your graph?

5) Show that t1/2= 0.693 can be found from the equation N=N0e-kt using the fact that N=1N0?

6) Why is it not possible to predict when any particular single radioactive nucleus will decay?

Conclusion

Write a concluding statement, based on your results, that relates to the purpose of the experiment?