What element, found in all plants and animals, is used by scientists to determine approximate dates for an artifact’s age?

its called "carbon"..

and the process of determining how old a plant or animal is called "carbon dating"

The element used by scientists to determine the approximate dates for an artifact's age is carbon. More specifically, they use Carbon-14, a radioactive isotope of carbon.

To understand how it works, we need to explain the process of carbon dating. Carbon-14 is formed in the atmosphere when cosmic rays collide with nitrogen atoms. These carbon-14 atoms mix with the regular carbon-12 atoms in the air and are absorbed by plants through photosynthesis. Animals then consume plants, and this carbon-14 is incorporated into their tissues.

The ratio of carbon-14 to carbon-12 in the atmosphere and living organisms remains relatively constant during their lifetime. However, once an organism dies, it no longer takes in carbon-14. From that point on, the carbon-14 decays over time, with a half-life of approximately 5730 years.

By measuring the ratio of carbon-14 to carbon-12 in an artifact or remains of an organism, scientists can estimate how long it has been since that organism died. This estimation is done by comparing the artifact's carbon-14 ratio to the known carbon-14 ratio in the atmosphere for a specific time period.

The process involves taking a small sample from the artifact, such as wood or bone, and analyzing it using a technique called accelerator mass spectrometry (AMS). This technique measures the ratio of carbon-14 to carbon-12 with high precision.

By comparing the measured ratio to the atmospheric ratio and considering the half-life of carbon-14, scientists can calculate the approximate age of the artifact, usually up to around 50,000 years. This method is widely used in archaeology, anthropology, and other fields to determine the age of organic materials.