Explain the term half-life. A sample of carbon is mainly carbon-12 which is not radioactive, and a small proportion of carbon-14 which is radioactive. When a tree is cut down the carbon-14 present in the wood at that time decays by beta emission. Write a nuclear equation to represent the decay of carbon-14. An ancient wooden cup from an archaeological site has an activity of 2.1 Bq. The corresponding activity for newly cut wood is 8.4 Bq. If the half-life of carbon-14 is 5730 years, estimate the age of the cup. Name an instrument used to measure the activity of a sample. What is the principle of operation of this instrument?

Leaving Cert Physics The Atom & Radioactivity: Explain the term half-life. A

Explain the term half-life - Leaving Cert Physics - Question 12(d) - 2007

Question 12(d)

Explain the term half-life. A sample of carbon is mainly carbon-12 which is not radioactive, and a small proportion of carbon-14 which is radioactive. When a tree ... show full transcript

Worked Solution & Example Answer:Explain the term half-life - Leaving Cert Physics - Question 12(d) - 2007

Step 1

Explain the term half-life.

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Answer

Half-life is defined as the time required for half of the radioactive nuclei in a sample to decay. This decay results in a decrease in the activity of the sample over time, reflecting the constant nature of radioactive decay. Mathematically, the relationship can be expressed as:

$t_{1/2} = \frac{0.693}{\lambda}$

where $t_{1/2}$ is the half-life, and $\lambda$ is the decay constant.

Step 2

Write a nuclear equation to represent the decay of carbon-14.

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Answer

$^{14}_{6}C \rightarrow ^{14}_{7}N + \beta^- + \overline{ u}$

In this equation, carbon-14 decays into nitrogen-14, emitting a beta particle and an antineutrino.

Step 3

Estimate the age of the cup.

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Answer

The activity of the wood from the archaeological cup is 2.1 Bq, while the activity of newly cut wood is 8.4 Bq. The ratio of these activities is:

$\frac{8.4 \text{ Bq}}{2.1 \text{ Bq}} = 4$

This indicates that the cup is four half-lives old, leading to:

$4 \times 5730 \text{ years} = 22920 \text{ years}$

Therefore, the estimated age of the cup is approximately 22,920 years.

Step 4

Name an instrument used to measure the activity of a sample.

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Answer

One common instrument used to measure the activity of a sample is a Geiger Counter (or GM tube).

Step 5

What is the principle of operation of this instrument?

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Answer

The Geiger Counter operates on the principle of ionization. When radioactive particles enter the tube, they ionize the gas inside, creating pairs of charged particles. These charged particles result in a current pulse that can be counted or displayed, allowing for the measurement of radioactivity.

Explain the term half-life - Leaving Cert Physics - Question 12(d) - 2007

Worked Solution & Example Answer:Explain the term half-life - Leaving Cert Physics - Question 12(d) - 2007

Explain the term half-life.

Write a nuclear equation to represent the decay of carbon-14.

Estimate the age of the cup.

Name an instrument used to measure the activity of a sample.

What is the principle of operation of this instrument?

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