5.2.4.1 Half-life calculations WS
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The half-life of carbon-14 is 5800 years.

A piece of wood contained 20 000 carbon-14 atoms when it was buried in a landslide.

Calculate the number of years it takes until the number of carbon-14 atoms in the wood is 2500.
4 points
A sample contains 8.0×10¹² atoms of a radioactive isotope of plutonium. The half-life of this isotope of plutonium is 14 years.

Calculate the number of atoms of this isotope of plutonium remaining in the sample after 28 years.

Give your answer in the form 𝑎x10^𝑏 and to two significant figures.
3 points
A sample of a radioactive material is placed near a radiation detector. A count-rate of 4800 counts/s is detected from the sample. After 36 hours the count-rate has fallen to 600 counts/s.

Calculate how many more hours must pass for the count-rate to become 150 counts/s.
3 points
Astatine-210 is a radioactive material. It has a half-life of 8 hours.

The mass of a sample of astatine-210 is 0.500kg.

Calculate how long it takes for 0.375kg of the sample to decay in hours.
3 points
A radioactive substance has a half-life of 120 hours.

Calculate the time for it to decay to 25% of its original amount in hours.
2 points
A radioactive isotope has a half-life of 6.0 years.

A sample of this isotope has a mass of 12mg.

Calculate the mass of this isotope that remains in the sample after 18 years in mg.
3 points
Americium-241 is a radioactive isotope. It has a half-life of 400 years.

A sample contains americium-241. Calculate the percentage of americium-241 that remains in the sample after 800 years have passed.
2 points
The isotope radon-220 is radioactive.

The half-life of radon-220 is 56s.

A sample of this isotope contains 7.2×10⁶ atoms.

Predict the number of 𝛼-particles that the radon-220 in the sample emits in the next 168s.

Give your answer in the form 𝑎x10^𝑏 and to two significant figures.
3 points
Thorium is radioactive and has a half-life of 26 hours. At a certain time, a pure sample of this isotope initially contains 4.8×10⁹ atoms.

Calculate the number of atoms of this sample that decay in the following 52 hours.

Give your answer in the form 𝑎x10^𝑏 and to two significant figures.
3 points
With no radioactive sample present, a scientist records a background radiation count of 40 counts/min.

The scientist brings a radioactive sample close to the detector. The count rate increases to 200 counts/min.

After 24 days the count rate is 50 counts/min.

Calculate the half-life of the radioactive sample in days.
1 point
The half-life of iridium-194 is 19 hours. A sample of iridium-194 has an initial count-rate of 1100 counts/min.

Calculate the count-rate from this sample after 38 hours in counts/min.
2 points
A sample of rock includes some uranium-239.

The half-life of uranium-239 is 23 minutes.

Determine the fraction of the uranium-239 that remains after 46 minutes.
2 points
Scientists use carbon-14 to estimate the age of wood that is very old.

A very old sample of wood contains 1.0×10⁸ carbon-14 atoms.

When the sample was new, it contained 8.0×10⁸ carbon-14 atoms.

The half-life of carbon-14 is 5700 years.

Estimate the age of the sample of wood in years.
3 points
An isotope of barium-137 has a half-life of 3 minutes.

A radioactive source contains 36mg of this isotope.

Calculate the mass of the isotope that remains in the source after 9 minutes in mg.
3 points
Carbon-14 is radioactive with a half-life of 5700 years.

An animal bone is dug up in an archaeological excavation. The quantity of carbon-14 in the bone is 25% of what it was when the bone was buried.

Calculate the time that has elapsed since it was buried in years.
2 points
Radon-222 is radioactive and has a half-life of 3.8 days.

At a certain time, a sample contains 6.4×10⁶ radon nuclei.

Calculate the number of α-particles emitted by the radon nuclei in the following 7.6 days.

Give your answer in the form 𝑎x10^𝑏 and to two significant figures.
3 points
The count rate of a radioactive sample is 2400 counts/min at 10am on one day. The half-life of the sample is two days.

Predict the count rate at 10am four days later in counts/min.
3 points
The half-life of radon-220 is 56s. A sample of radon-220 is in a container. After 112s the mass of radon-220 is 9.2mg.

Calculate the mass of the original sample in mg.
2 points
Radium-226 has a half-life of 1600 years.

A sample contains 8.0mg of radium-226.

Calculate the time for the sample to decay until only 1.0mg of radium-226 remains in years.
2 points
Americium-241 has a half-life of 432 years. A sample contains 16mg of americium-241.

Calculate the time it takes until only 4.0mg of americium-241 are left in the sample in years.
2 points
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