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In this lesson, we will learn how to calculate the activity of a radioactive sample after a given amount of time using the half-life of the isotope.

Q1:

A radioactive sample initially contains 2 . 4 0 × 1 0 − 2 mol of a radioactive material which has a half-life of 6.00 hours.

Approximately how many moles of the radioactive material remain after 6.00 h?

Approximately how many moles of the radioactive material remain after 12.00 h?

Approximately how many moles of the radioactive material remain after 36.00 h?

Q2:

A sample of radioactive material is obtained from a very old rock. A plot of the natural logarithm of the sample’s activity versus time yields a slope value of 1 . 0 0 × 1 0 s^{−1}. What is the half-life of this material?

Q3:

A piece of wood from an ancient Egyptian tomb is tested for its carbon-14 activity. It is found to have an activity per gram 𝐴 = 1 0 decay/min ⋅ g. What is the age of the wood? Use a value of 3 . 8 4 × 1 0 − 1 2 s^{−1} for the decay constant of carbon-14 and a value of 1 0 − 1 2 for the relative abundance of carbon-14.

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