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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).
By measuring the parent isotope (radioactive) and the daughter isotope (radiogenic) in a system (for example, a rock), we can tell how long the system has been closed (in our example, when the rock formed).
We have dated meteorites using Rb-Sr, Sm-Nd, Pb-Pb, Re-Os, and Lu-Hf isotope systems and have obtained very similar ages.
The fact that the age we calculate is reproducible for these different systems is significant.
Answer 2: Yes, radiometric dating is a very accurate way to date the Earth.
I should mention that the decay constants (basically a value that indicates how fast a certain radioactive isotope will decay) for some of these isotope systems were calculated by assuming that the age of the earth is 4.56 billion years, meaning that we will also calculate an age of 4.56 billion years if we use that decay constant.
This is an enormous branch of geochemistry called Geochronology.
It is an accurate way to date specific geologic events.
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.
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).