what are the distinct characteristic does radiocarbons depends on?

The characteristic is the battle of binding nuclear energy vs repulsive energy of the protons. This energy changes slightly on each individual particle as they shift in the nucleus, and at some point in time, the binding energy is insufficient to hold a particle in position, and that particle "explodes" and releases energy. Because this event is random, statistically, it ends up having a "mean" time, and we measure that by statistics, so each group of atoms will form a "half-life" of the decay process, which we measure and then predict macroscopic events.

thanks..

The ratio of C-12 to C-14 as a function of remaining activity => age of artifact.

- t∙k = ln(C-14/C-12); t = age of artifact
Note FYI: For living organic tissue, C-14 activity = C-12 activity. For dead organic tissue, C-14 activity < C-12 activity. At death of the organic tissue, C-14 decays to N-14 by beta emission, but C-12 does not decay resulting in C-14 activity < C-12 activity over time. The decay of C-14 follows 1st order decay (as does all radio decay process) giving A = A₀eˉᵏᵗ => -k∙t = ln(A/A₀) => t = ln(A/A₀)/-k = ln(C-14/C-12)/-k; k(C-14) = 0.693/5730 yrs = 1.21E-4 yrˉ¹.

Radiocarbon dating relies on the distinct characteristics of radiocarbon, also known as carbon-14. Here are the key factors that radiocarbon dating depends on:

1. Carbon-14 Production: Radiocarbon is continuously being formed in the Earth's atmosphere through the interaction of cosmic rays with nitrogen atoms. These cosmic rays cause the nitrogen atoms to transform into carbon-14.

2. Carbon-14 Decay: Radiocarbon is a radioactive isotope, which means it undergoes radioactive decay over time. This decay is known as beta decay, where a neutron is converted into a proton, causing the release of a beta particle (electron) and a neutrino.

3. Half-Life: The half-life of carbon-14 is the time it takes for half of the carbon-14 atoms in a sample to decay. The half-life of carbon-14 is approximately 5,730 years.

4. Carbon-14 Uptake: Living organisms, including plants and animals, constantly absorb carbon from the environment through processes like photosynthesis and consuming other organisms. As a result, they contain a certain concentration of carbon-14.

5. Carbon-14 Equilibrium: When an organism dies, it no longer takes in carbon-14 from the environment. Since the radioactive decay of carbon-14 continues, the concentration of carbon-14 in the remains of the organism gradually decreases over time.

By measuring the remaining concentration of radiocarbon in a sample, scientists can estimate the age of the sample by comparing it to known concentrations of radiocarbon during different periods in Earth's history. This method is commonly used in archaeology, anthropology, and geology to determine the age of organic materials up to around 50,000 years old.