Half -life

Name : Adam Okoe Mould Title : Determination of Half Life Criteria : DCP, CE Aim : To determine the half-life a model decay using cubes. Hypothesis : The probability that a die will decay ,that is land with the black spot on the top side, is 1/6. Therefore since the die is a fair die, the half-life would be 3.5 between 3 and 4. Raw Data Time / s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Number of Cubes Decayed at specific time 12 15 13 11 10 7 5 4 5 2 2 1 1 2 1 1 0 1 2 1 1 0 2 0 0 1

Numbers of Undecayed I

Number Of Undecayed

12 27 40 51 61 68 73 77 82 84 86 87 88 90 91 92 92 93 95 96 97 97 99 99 99 100

88 73 60 49 39 32 27 23 18 16 14 13 12 10 9 8 8 7 5 4 3 3 1 1 1 0

Graph of Number of Undecayed Against Time

86

y

76 66 56 46 36

y ca d n fU ero b m u N

26 16 6 x 2

4

6

8

10

12

14

Number of Throws [Time]

16

18

20

22

Now using this graph the first four half-lifes will be calculated starting from 80 Undecayed. Number of Undecayed 80 1 2 3 4

40 20 10 5

Time Half/s Life/s 1.00 5.23 9.48 13.73 17.99

4.23 9.48 8.50 8.50

The half-lifes obtained increased as time went on from 4.23 seconds to 9.48 seconds and then remained constant at 8.50s for the last 2 half-lifes

Conclusion

The half-life I agreed upon was 4.23 seconds from the graph of number of Undecayed against time. This was because when a greater number of die rather than a smaller number of die are used the probability of the outcome is as expected. Therefore, the disparity in the first half-life with the other three half-lifes which were 9.48s, 8.50s and 8.50s was due to the smaller number of die used in those intervals. Also from the graph, it can be deduced that as time goes on the rate of decay reduces since the gradient of the graph reduced as time went on. Sources of Error 1. When a small number of die is used it does not enable number of decayed dies to reflect the true probability that a die with a dot will face up. 2. Also, when the die were poured from the container the experimenter did not use the same method in doing so Improvements to the Investigation 1. A large number of die should be used so that the probability of the die would have a large affect on the number of decayed die. It would enable the actual number of decayed die reflect the probability of the die facing up with a dot. 2. The dice should be poured from the container in a constant motion. This can be done by quickly turning the container upside down about a fixed point in the air.