Half Life Calculations

The half life of a radioactive substance is the time taken for half the material to decay. Half the substance decays in every half life. We can't tell which half of the material will decay. If we pick an individual atom we only know there is a one in two chance that that atom will decay in one half life.  This is because radioactivity is a completely random process. In fact, so random is it that we cannot say with certainty that half the substance will decay, only that we should expect half the ,materuial to decay.

If we start out with 80 grams of some radioactive substance with a half life T years, we can draw up a table showing how much of the substance we would expect NOT to have decayed after each time period T years.

Time in years

Mass of Undecayed Substance Remaining (grams)

0

80

T

40

2T

20

3T

10

4T

5

The process of decay will continue until all the substance has decayed.

We can work out the half life of a substance by looking at how much of a material remains undecayed from an initial mass. Suppose we know that 480 grams of a material has decayed to 15 grams in 50 years. We can draw up a table like the one above to find how many half lives this decay has taken.

Time in years

Mass of Undecayed Substance Remaining (grams)

0

480

T

240

2T

120

3T

60

4T

30

5T

15

The decay has taken five half lives soyears so

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