Radioactive isotope used for radiometric dating
It is commonly used in earth science to determine the age of rock formations or features or to figure out how fast geologic processes take place (for example, how fast marine terraces on Santa Cruz island are being uplifted).
Radiometric dating relies on the principle of radioactive decay.
We call the original, unstable isotope (Uranium) the "parent", and the product of decay (Lead) the "daughter".
From careful physics and chemistry experiments, we know that parents turn into daughters at a very consistent, predictable rate.
A mass spectrometer is an instrument that separates atoms based on their mass.The reason that I trust the accuracy of the age that we have determined for the earth (~4.56 billion years) is that we have been able to obtain a very similar result using many different isotopic systems.Most estimates of the age of the earth come from dating meteorites that have fallen to Earth (because we think that they formed in our solar nebula very close to the time that the earth formed).Uranium eventually decays into lead, and lead does not normally occur in zircon, except as the radioactive decay product of uranium.Therefore, by measuring the ratio of lead to uranium in a crystal of zircon, you can tell how much uranium there originally was in the crystal, which, combined with knowing the radioactive half-life of uranium, tells you how old the crystal is.
There are many radiometric clocks and when applied to appropriate materials, the dating can be very accurate.