On the other hand, the sedimentary rock (as I know) usually provide the time of formation by age range of fossil e.g. Is there any method to make it more specific like the crystalline one?
Although the time at which any individual atom will decay cannot be forecast, the time in which any given percentage of a sample will decay can be calculated to varying degrees of accuracy.
Given isotopes are useful for dating over a range from a fraction of their half life to about four or five times their half life.
The time that it takes for half of a sample to decay is known as the half life of the isotope.
Some isotopes have half lives longer than the present age of the universe, but they are still subject to the same laws of quantum physics and will eventually decay, even if doing so at a time when all remaining atoms in the universe are separated by astronomical distances.
During the 1990s these dates were systematically re-assessed as the technique became better understood, and many problems were found with earlier dates.
For example, it was realised that radiocarbon dates obtained from charcoal fragments were often unreliable: the wood could have come from a tree that was hundreds of years old when it was burnt, and so an occupation site would seem much older than it really was.
Various elements are used for dating different time periods; ones with relatively short half-lives like carbon-14 (or C) are useful for dating once-living objects (since they include atmospheric carbon from when they were alive) from about ten to fifty thousand years old. Longer-lived isotopes provide dating information for much older times.
The key is to measure an isotope that has had time to decay a measurable amount, but not so much as to only leave a trace remaining.
Absolute dating is necessary for knowing specific time e.g.
by isotope K/Ar in mica, especially in the crystalline rock: igneous and metamorphic rock.
where is the half-life of the element, is the time expired since the sample contained the initial number atoms of the nuclide, and is the remaining amount of the nuclide.