Radioactive decay series1 When an unstable nucleus undergoes radioactive decay, the nucleus produced may be

still unstable.2 The daughter nuclide will then undergo another radioactive decay (or may be several

times) until a stable nucleus is produced.3 This produces a series of radioactive decay known as radioactive decay series.4 Example

Half-life1 During a radioactive decay, an unstable nucleus becomes a more stable nucleus in a

process that occurs randomly and spontaneously.2 As a result, the number of unstable nucleus in a sample of radioactive substance

decreases with time.3 The half-life of a radioactive sample is defined as the time taken for the number of

unstable nucleus in the sample to be reduced to half of its original number. 4 Example

5 The half-life for a radioactive sample is a constant because(a) Radioactive decay occurs randomly(b) Large number of nuclei in the radioactive sample are involved in a radioactive

decay

6 Assume that is the original number of unstable atoms.

After one half life, the number of unstable atoms, becomes ,

After another half-life, the number of unstable atoms, becomes and so on. 7 Hence, after n half-lives, the number of unstable atoms remaining is N.

where

number of unstable atoms remaining

number of unstable atoms initially

number of half-lives involved = 8 Radioactive decay curve

9 Problem solving(a) A radioactive sample contains 600 billion unstable atoms. One hour later, the

number of unstable atoms reduces to 75 billion atoms. Calculate the half-life of this radioactive sample.

(b) A sample of sodium-24 contains 40 million atoms. After 2 days, the number of sodium-24 atoms reduces to 5 million atoms. Calculate the half-life of sodium-24.

(c) The mass of a radioactive substance reduces from 32 g to 1 g in 100 days. Calculate the half- life of the radioactive substance.

(d) The activity of a radioactive substance reduces to 6.25 % of its original activity in 60 years. Determine the half-life of this radioactive substance.

(e) The activity of a radioactive sample reduces to 12.5 % of its original activity in 6 days. Calculate the half-life of the radioactive substance.

(f) Given that the half-life of radon-222 is 3.8 days, how long is required for 320 g of radion-222 to reduce its mass by 310 g?

(g) The half-life of a radioactive substance X is 5 days. Calculate the time required for 96 g of X to reduce its mass by 90 g.

(h) The activity of a radioactive substance with a half-life of 3 days is recorded as 24 counts per second. What is the activity of the radioactive substance 15 days ago?

(i) The GM tube detects the activity of a radioactive substance as 42 counts per second. If the half-life of the radioactive substance is 4 hours, what is the activity of this radioactive substance 1 day ago?

(j) An archaeologist successfully dug out some bones, believed to belong to the first man on earth. A test found that the activity of carbon-14 in the bones is 34 counts per second. If the original activity of carbon-14 in the bones is 4352 counts per second, how old is the bones? [Half-life of carbon-14 = 5700 years]

(k) During an expedition into the Pacific Ocean, a scientist found an old rock. A test was conducted on the rock and found that the activity of plutonium-239 in the rock is 3.125 % of its original activity. If the half-life of plutonium-239 is 24000 years, how old is the rock?

(l) The graph below shows the decay curve for a radioactive substance Y.

(i) What is the half-life of substance Y?(ii) Determine the value of t.

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