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Radioactive decay and half-life - CCEACalculating the isotope remaining

Radioactivity was first noticed by French physicist, Henri Becquerel, in 1896, when he observed that some photographic plates which had been stored close to a uranium compound had become partly exposed or 鈥榝ogged鈥.

Part of Physics (Single Science)Atomic and nuclear physics

Calculating the isotope remaining

It should also be possible to state how much of a sample remains or what the activity or count should become after a given length of time.

This could be stated as a fraction, decimal or ratio.

For example the amount of a sample remaining after four half-lives could be expressed as:

  • a fraction - a \(\frac{\text{1}}{\text{2}}\) of a \(\frac{\text{1}}{\text{2}}\) of a \(\frac{\text{1}}{\text{2}}\) of a \(\frac{\text{1}}{\text{2}}\) remains which is \(\frac{\text{1}}{\text{2}}\) x \(\frac{\text{1}}{\text{2}}\) x \(\frac{\text{1}}{\text{2}}\) x \(\frac{\text{1}}{\text{2}}\) = \(\frac{\text{1}}{\text{16}}\) of the original sample.
  • a decimal - \(\frac{\text{1}}{\text{16}}\) = 0.0625 of the original sample

This could then be incorporated into other data. So, if the is two days, four half-lives is 8 days.

Question

If a sample with a half-life of 2 days has a count rate of 3,200 Bq at the start, what is its count rate after 8 days?

Question

The half-life of cobalt-60 is 5 years. If there are 100 g of cobalt-60 in a sample, how much will be left after 15 years?

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