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Radioactive decay for AQA A-level Physics

Radioactive decay

This page covers the following topics:

1. Radioactive decay
2. Constant decay probability
3. Calculating activity

A nucleus is said to be stable if it has a certain amount of neutrons depending on the number of protons it has. If there are too many or too few neutrons, the nucleus is said to be unstable and will decay by emitting radiation. The same number of protons and neutrons are needed for nuclei of elements of fewer protons to be stable. The greater the number of protons, the more neutrons are needed for the nucleus to be stable. Radioactive decay occurs randomly and each decay is independent of the rest, therefore predictions about when an atom will decay cannot be made.

Radioactive decay

The decay constant, given by ฮป, is the probability of a given nucleus decaying per second. It is measured in sโปยน. It is calculated using the following formula: tโ‚/โ‚‚ = ln2/ฮป, where tโ‚/โ‚‚ is the half time of the isotope. The half time is defined as the time taken for the mass of an isotope to be halved or the time taken for its activity to be halved.

Constant decay probability

The greater the time that has passed, the smaller the number of nuclei present, therefore the decay of the sample of the object will decrease. The number of decaying nuclei is directly proportional to the original number of them present. This can be expressed through the following formula: A = Aโ‚€exp(โˆ’ฮปt), where Aโ‚€ is the initial activity and ฮป is the decay constant. Activity can also be calculated using the following formula: A = ฮปN, where N is the number of nuclei present.

Calculating activity

1

Given that the number of nuclei present in a radioactive sample with decay constant of 3.5 ร— 10โปโถ sโปยน after 20 minutes is 6.8 ร— 10โธ, calculate the initial activity of the sample.

Using A = ฮปN, A = 3.5 ร— 10โปโถ sโปยน ร— 6.8 ร— 10โธ = 2380 Bq. 20 minutes = 1200 seconds. Using A = Aโ‚€exp(โˆ’ฮปt), 2380 Bq = Aโ‚€ ร— exp(-3.5 ร— 10โปโถ sโปยน ร— 1200 s), so Aโ‚€ = 2390 Bq (to the nearest integer).

Given that the number of nuclei present in a radioactive sample with decay constant of 3.5  ร— 10โปโถ sโปยน after 20 minutes is 6.8 ร— 10โธ, calculate the initial activity of the sample.

2

Define the half-time of an isotope.

Half time is defined as the time taken for the mass of an isotope to be halved or the time taken for its activity to be halved.

Define the half-time of an isotope.

3

Calculate the initial activity of a sample with a decay constant of 4.7 ร— 10โปโถ sโปยน. The number of nuclei present in the sample after 45 minutes is found to be 4.2 ร— 10โธ.

Using A = ฮปN, A = 4.7 ร— 10โปโถ sโปยน ร— 4.2 ร— 10โธ = 1974 Bq. 45 minutes = 2700 seconds. Using A = Aโ‚€exp(โˆ’ฮปt), 1974 Bq = Aโ‚€ ร— exp(-4.7 ร— 10โปโถ sโปยน ร— 2700 s), so Aโ‚€ = 1999 Bq (to the nearest integer).

Calculate the initial activity of a sample with a decay constant of 4.7  ร— 10โปโถ sโปยน. The number of nuclei present in the sample after 45 minutes is found to be 4.2 ร— 10โธ.

4

The initial number of atoms present in an isotope are 7.2 ร— 10โน. Given that its decay constant is 1.85 ร— 10โปโถ sโปยน, calculate the initial activity of the isotope.

Using A = ฮปN, A = 1.85 ร— 10โปโถ sโปยน ร— 7.2 ร— 10โน = 13320 Bq.

The initial number of atoms present in an isotope are 7.2 ร— 10โน. Given that its decay constant is 1.85 ร— 10โปโถ sโปยน, calculate the initial activity of the isotope.

5

What is the relationship between the number of decaying nuclei and the original number of them present?

The number of decaying nuclei is directly proportional to the original number of them present.

What is the relationship between the number of decaying nuclei and the original number of them present?

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