Carbon- 14 , present within living organisms and substances derived from living organisms, is often used to establish the age of fossils and artifacts. Determine the number of protons and neutrons in a carbon- 14 isotope and write its symbol in the form \({ }_{Z}^{A} X\).

Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons in their nuclei. This means that while they share the same atomic number, they have different mass numbers.

Take carbon as an example. All carbon atoms have 6 protons, which is identified by the atomic number. However, the number of neutrons can vary, leading to different isotopes like Carbon-12, Carbon-13, and Carbon-14. These numbers, 12, 13, and 14, are the mass numbers of the isotopes. Despite these differences, all carbon isotopes behave similarly in their chemical properties because they have the same electronic structure, which is dictated by the number of protons.

The atomic number of an element is a fundamental characteristic that defines the type of atom. It indicates the number of protons present in the nucleus of an atom. Since each element has a unique number of protons, the atomic number also serves as an identifier for the element.

In the Periodic Table of Elements, the elements are arranged in order of increasing atomic number. For example, the atomic number of carbon is 6, which means regardless of the isotope, whether it's Carbon-12 or Carbon-14, every carbon atom contains 6 protons.

Neutrons play a critical role in the formation of isotopes. They contribute to the mass of an atom but do not affect the chemical properties since they are electrically neutral. The number of neutrons in an atom's nucleus can change without altering the type of element it is, which leads to the creation of different isotopes of the same element.

To identify the number of neutrons in an isotope, you subtract the atomic number from the mass number, as in the case of Carbon-14. Carbon-14 has a mass number of 14, and an atomic number of 6, so it has 14 - 6 = 8 neutrons. Understanding the neutron count is important not only for identifying isotopes but also for understanding nuclear stability and isotopic behaviors.

Radioactive dating, or radiometric dating, is a method used to date materials such as rocks or carbon, by comparing the abundance ratio of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay.

The isotope Carbon-14 is used in the dating of organic matter because it is constantly being created in the atmosphere via cosmic rays and is incorporated into living organisms. Carbon-14 is radioactive and decays over time. By measuring the amount of Carbon-14 that remains in a fossil or artifact and comparing it to the current levels found in the atmosphere, scientists can determine the approximate age of the object. The decay of Carbon-14 is like a clock that starts ticking when the organism dies, and by understanding this process, we can uncover information about the past.