Activity and half-life calculations (including complex ones)

Physics

In A-level physics, some pupils will build on this knowledge to learn about probability and half-life equations, nuclear instability, Einstein’s equation E = mc2 that links mass and energy, and controlled nuclear fission.

In the Periodic table unit, in chemistry, pupils learnt about the nuclear model of the atom, the atomic number and mass number, and about isotopes of elements.

This unit covers atomic structure, isotopes, radioactive decay, and half-life. It explores alpha, beta, and gamma radiation, nuclear fission and fusion, and the uses of radiation in medicine, highlighting differences between contamination and irradiation.

Nuclear physics

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the rate at which the sample emits radiation.

The activity of a sample of a radioactive isotope is …

there are 100 radioactive nuclei in a sample.

100 nuclei decay after each half–life has passed.

An activity of 100 becquerel (Bq) means …

The time it takes for its activity to fall to half of its initial value.

Half the time it takes for its activity to fall to zero.

The time it takes for half of the nuclei to decay.

Half the time it takes for all of the nuclei to decay.

The time it takes for half of a nucleus to decay.

Which of the following can be used to define what is meant by the half–life of a radioactive isotope?

Sodium–24 has a half–life of 15 hours. If a sample of sodium–24 originally has an activity of 500 Bq, what fraction of its original activity will remain after 30 hours?

After 42 days the activity of a sample of phosphorus–32 has decreased from 400 Bq to 50 Bq. What is the half–life of phosphorus–32?

The half–life of protactinium–234 is 6.75 hours. What percentage of the original sample will have decayed after 13.5 hours?

It takes 30 minutes for all of the nuclei to decay.

It takes 15 minutes for one nucleus to decay.

It takes 15 minutes for half of the nuclei to decay.

Which of the following describes what is meant by a radioactive isotope having a half–life of 15 minutes?

All radioactive isotopes have the same half–life.

Isotopes of the same element have the same half–life. 

Half–life values vary between different isotopes and elements.

Half–life does not depend on the radioactive isotope.

How do the half–lives of different radioactive isotopes compare?

Increasing the temperature increases the half–life.

Increasing the temperature decreases the half–life.

Increasing the temperature has no effect on the half–life.

What effect does increasing the temperature have on the half–life of a radioactive isotope?

plutonium–239: half–life = 24,100 years

hydrogen–3 (tritium): half–life = 12.3 years

polonium–214: half–life = 0.16 milliseconds

Starting with the longest, sort the following radioactive isotopes into order of decreasing half–life.

It is longer when part of the CO molecule.

It is longer when part of the CO₂ molecule.

It is the same, regardless of the molecule it is part of.

How does the half–life of a carbon–14 atom in a carbon monoxide (CO) molecule compare to its half–life in a carbon dioxide (CO₂) molecule?

A radioactive isotope has a half–life of 10 hours. Match each of the following fractions of the sample remaining to the correct amount of time that has passed.

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