Uses of uranium lead dating
The process of radiogenic dating is usually done using some sort of mass spectrometer.
A mass spectrometer is an instrument that separates atoms based on their mass.
This is an enormous branch of geochemistry called Geochronology.
It is an accurate way to date specific geologic events.
Obviously, if the substance you are measuring is contaminated, then all you know is the age since contamination, or worse, you don't know anything, because the contamination might be in the opposite direction - suppose, for example, you're looking at radio carbon (carbon 14, which is produced in the atmosphere by cosmic rays, and which decays into nitrogen).
Since you are exposed to the atmosphere and contain carbon, if you get oils from your skin onto an archeological artifact, then attempting to date it using radio carbon will fail because you are measuring the age of the oils on your skin, not the age of the artifact.
All radioactive isotopes have a characteristic half-life (the amount of time that it takes for one half of the original number of atoms of that isotope to decay).
Radiometric dating relies on the principle of radioactive decay.
For example, a problem I have worked on involving the eruption of a volcano at what is now Naples, Italy, occurred 38500 years ago with a plus or minus of 300 years.
So, when the materials are appropriate and one carefully avoids contamination and re setting radiometric clocks can be VERY ACCURATE.
The ratio of the parent to daughter then can be used to back-calculate the age of that rock. The reason we know that radiometric dating works so well is because we can use several different isotope systems (for example, Uranium-Lead, Lutetium-Halfnium, Potassium-Argon) on the same rock, and they all come up with the same age.
This gives geologists great confidence that the method correctly determines when that rock formed.