Of course, there are many problems with such dating methods, such as parent or daughter substances entering or leaving the rock, as well as daughter product being present at the beginning.
Here I want to concentrate on another source of error, namely, processes that take place within magma chambers.
Because the number of atoms in a typical laboratory sample is extremely large, methods involving the use of radioactivity are among the most sensitive in all science.
The time it takes for half of a sample of one kind of nucleus (called a nuclide, the time is called a half-life) is normally constant, which allows the dating of materials by looking at how much of a sample has decayed and working out, sometimes with very good accuracy, how long it would have taken for that to happen. It is worthwhile to clarify the definitions of three terms that are often conflated: Chernobyl, or Fukushima are often described as having released enormous amounts of "radioactivity", or worse yet "radiation", when in fact their most significant (and destructive) effect was the release of enormous amounts of radioactive contaminants that caused large areas to become radioactive, and entered the environment and food chain to contaminate plant and animal life (including humans).
These long time periods are computed by measuring the ratio of daughter to parent substance in a rock and inferring an age based on this ratio.
This age is computed under the assumption that the parent substance (say, uranium) gradually decays to the daughter substance (say, lead), so the higher the ratio of lead to uranium, the older the rock must be.
One rare form has atoms that are 14 times as heavy as hydrogen atoms: carbon-14, or C ratio gets smaller.
The first one is biblical literalists, specifically young Earth creationists and some old Earth creationists, because the extent of decay of radioactive elements found on Earth, such as uranium and potassium, suggests that Earth is billions of years old. The second group is the anti-nuclear movement, which considers radioactivity that results from the use of nuclear power to be very dangerous and a menace to humans, even though it's actually a tiny drop in the sea of natural radioactivity.
Activities of the anti-nuclear movement are partially responsible for the pervasive fear of radiation present in most Western societies.
Clearly, such huge time periods cannot be fitted into the Bible without compromising what the Bible says about the goodness of God and the origin of sin, death and suffering—the reason Jesus came into the world (See Six Days? He said, This only makes sense with a time-line beginning with the creation week thousands of years ago.
It makes no sense at all if man appeared at the end of billions of years.