Final answer:
Radioactive decay is the process by which an unstable nucleus loses energy, and it is calculated using the decay constant and half-life. Geologists use radiometric dating based on radioactive decay to determine the age of geological materials.
Step-by-step explanation:
Understanding Radioactive Decay
Radioactive decay is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This decay process can result in a change in the number of protons in the nucleus and, consequently, transform the original element into a different one. To calculate radioactive decay, scientists use a formula that incorporates the decay constant (λ), which represents the likelihood of decay of a nucleus per unit time. The relationship between the half-life (T1/2), which is the time taken for half of the radioactive nuclei in a sample to decay, and the decay constant is given by T1/2 = ln(2)/λ.
For instance, with cobalt-60, which is a radioactive isotope of cobalt, you would use its known half-life and decay constant to calculate the fraction of a sample remaining after a given time period, such as 15 years. The equation used is N(t) = N0e-λt, where N(t) represents the amount of substance that remains after time (t), N0 is the initial quantity of the substance, and e is the base of the natural logarithm.
Geologists often utilize radioactive decay in radiometric dating techniques to determine the ages of rocks, minerals, and fossils. By measuring the ratio of parent to daughter isotopes and knowing the decay rate, they can ascertain how long ago the rock or fossil formed. This is crucial for constructing the geologic history of Earth and understanding the timing of events that have shaped our planet's surface and environment.