University of Michigan - Department of Astronomy

Version: half-life

Geologic Age

Radiometric Dating Using the Half Life Method

Information you need to complete this is in the Introduction

Part 1: Half-life

  1. What is half-life?

  2. How much of the parent isotope is left after one half life has elapsed?

  3. If there was no daughter isotope in the beginning, how much daughter isotope will there be after 1 half life has elapsed?

  4. What is the daughter-parent ratio after one half life?

  5. What is the daughter-parent ration after 2 half lives? Explain/show your work.

The graph below shows the relationship between the daughter-parent ratio and the number of half lives elapsed.

Half life graph

Using this graph, you can determine the age of a few samples.

  1. Calculate the daughter to parent ratio for the samples in table 2.1. Enter the values in table 2.1.
  2. Use the graph to determine the number of half-lives that passed for each sample. Enter your answers in the table.
Table 2.1




Half-lives elapsed

Age (Gyr)







Determining the Age

The parent-daughter ratio and half-lives elapsed hold no matter what minerals you are dealing with. To determine the age, you need to know what the minerals are, and the half-life of the parent. Spectroscopy is used to determine what the minerals are, and how much there is (you saw how to recognize the element in a gas in the spectroscopy lab - with a better spectroscope you can also determine the density and from that the number of particles.) The half life of isotopes is determined by theory, and confirmed with controlled experiments.

  1. How do you calculate the age of a sample given the number of half-lives elapsed and the half life of the parent?

  2. Calculate the age of the rocks if the parent is potassium-40, which has a half life of is 1.26x109 years (1.26 Gyr). Record your answers in the table. (Note this assumes that Dt is the total amount of daughter isotopes)
  3. What is/are the daughter isotope(s) of K-40?

  4. What is assumed about the initial value of the daughter isotope D0?

  5. Why is it safe to make this assumption about D0?

Last modified: 2/19/08 by SAM with material/suggestions from EP

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