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 carbon-14 and write its symbol in the form \({ }_{Z}^{A} \mathrm{X}\).

The atomic number, represented by the symbol 'Z', is a fundamental concept in chemistry and physics. This number denotes the amount of protons in the nucleus of an atom, which determines the element's identity. For example, carbon always has an atomic number of 6, meaning every carbon atom contains six protons.

It's important to know that the atomic number is unique to each element. As a quick reference, the periodic table lists all elements in order of increasing atomic number. In the case of the exercise with carbon-14, the atomic number helps us to understand that despite changes in the number of neutrons, the element remains carbon due to its constant number of protons.

The mass number, or atomic mass, is denoted as 'A', and it represents the total number of protons and neutrons in an atom's nucleus. To find the mass number, just add up these particles. It's essential for determining isotope varieties since isotopes of an element have the same number of protons but different numbers of neutrons.

When you're looking at a nuclide symbol, like those used in our carbon-14 exercise, the mass number goes at the top left. It's not to be confused with the atomic weight, which is the average mass of all an atom's isotopes and may include decimal values. Mass number, however, is always a whole number since it's a tally of individual proton and neutron particles.

Isotopes are versions of a chemical element that have the same number of protons (and thus the same atomic number) but different numbers of neutrons. This results in different mass numbers. While the atomic number is the identity card of an element, the mass number tells us more about the specific version of that element.

For instance, carbon-12 and carbon-14 are isotopes of carbon—both have six protons but differ in their neutron count. This distinction is important in many scientific fields, like archaeology for carbon dating, which depends on the decay of carbon-14 to determine the age of ancient organic materials.

Neutrons play a key role in the world of isotopes. They add mass but don't change the element's identity, which is determined by the atomic number (the number of protons). In the case of carbon-14, to find the number of neutrons, you subtract the atomic number from the mass number: \(14 - 6 = 8\) neutrons.

Neutrons add nuance to our understanding of elements because their number can vary widely within the same element. These variations lead to isotopes with unique physical and chemical properties, such as different stability and radioactive decay rates. Knowing the neutron count in isotopes is instrumental in fields like nuclear physics, chemistry, and geochronology.