The amount of carbon-14 in ancient artifacts and fossils is often used to establish their age. Determine the number of protons and the number of neutrons in a carbon-14 isotope and write its symbol in the form AZX.

The atomic number is a fundamental property of each element, representing the number of protons in the nucleus of an atom. Protons carry a positive charge and are one of the essential components of atoms, along with neutrons and electrons. The atomic number is crucial because it not only defines the element itself but also determines its position within the Periodic Table of Elements.

For carbon, the atomic number is always 6, meaning every atom of carbon has six protons in its nucleus, regardless of its isotope. This consistency makes the atomic number a reliable identifier for elements. It's important to note that while the number of neutrons can vary among isotopes, the number of protons, and thereby the atomic number, remains fixed for a given element.

The mass number is the total count of protons and neutrons in an atom's nucleus. Since protons and neutrons are collectively known as nucleons, the mass number is essentially the nucleon count. Unlike the atomic number, the mass number can vary among different isotopes of the same element because isotopes have different numbers of neutrons.

For example, the mass number of carbon-14 is 14, indicating it has a total of 14 protons and neutrons combined. This is different from, say, carbon-12, which has 12 nucleons. The mass number plays a crucial role in isotopic notation and significantly influences the atomic mass of an element.

To calculate the number of neutrons in an isotope, you subtract the atomic number from the mass number. Neutrons are uncharged particles in the nucleus, and their number can vary in the isotopes of an element, giving rise to different physical properties.

For instance, in carbon-14, the process involves taking the mass number 14, which includes both protons and neutrons, and subtracting the atomic number of 6, which represents just the protons: \( 14 - 6 = 8 \). This leaves us with 8 neutrons in carbon-14. It's a straightforward calculation, yet it's fundamental in understanding the structure of isotopes and the concepts of atomic mass and stability.

Standard nuclear notation is used to represent the composition of a particular isotope succinctly. It includes the mass number (A) at the upper left, the atomic number (Z) at the lower left, and the chemical symbol (X) to the right. This notation provides at a glance the information needed to identify the isotope uniquely.

For carbon-14, the standard nuclear notation is \( _6^{14}C \). Here, the atomic number 6 (\( Z \)) indicates the proton count and carbon's place in the Periodic Table, while the mass number 14 (\( A \)) reveals the sum of protons and neutrons in the nucleus. This concise representation is widely used in chemistry and physics to describe isotopes and nuclide characteristics.