How do we know radiometric dating is reliable
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).
They can then look at a single mineral, and using an instrument called a mass spectrometer, they can measure the amount of parent and the amount of daughter in that mineral.For example, the element Uranium exists as one of several isotopes, some of which are unstable.When an unstable Uranium (U) isotope decays, it turns into an isotope of the element Lead (Pb).There are many radiometric clocks and when applied to appropriate materials, the dating can be very accurate.As one example, the first minerals to crystallize (condense) from the hot cloud of gasses that surrounded the Sun as it first became a star have been dated to 4568 plus or minus 2 million years....!! Other events on earth can be dated equally well given the right minerals.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).
Because geochronologists want to measure isotopes with different masses, a mass spectrometer works really well for dating things.
I do think that radiometric dating is an accurate way to date the earth, although I am a geochronologist so I have my biases.
Hope that helps, and please ask if you'd like more details! I think that I will start by answering the second part of your question, just because I think that will make the answer to the first question clearer.
Radiometric dating is the use of radioactive and radiogenic (those formed from the decay of radioactive parents) isotopes (isotopes are atoms of the same element that have different numbers of neutrons in their nuclei) to determine the age of something.
We have dated meteorites using Rb-Sr, Sm-Nd, Pb-Pb, Re-Os, and Lu-Hf isotope systems and have obtained very similar ages.