How many neutrons are found in \({ }^{12} \mathrm{C}\) ? \({ }^{13} \mathrm{C} ?^{13} \mathrm{C}^{-}\) ?

In the vast universe of chemistry, the concept of isotopes stands out as a fundamental component of atomic structure. Isotopes are different forms of the same element that contain the same number of protons but differ in the number of neutrons. This variance in neutron count does not affect the chemical properties of an element, as these are primarily dictated by the number of protons, which defines the element itself. However, isotopes can exhibit differences in physical properties, such as stability and mass.

For instance, take the element carbon: it has two stable isotopes commonly found in nature – Carbon-12 ({ }^{12} {C}) and Carbon-13 ({ }^{13} {C}). Both share six protons, matching the atomic number of carbon, but their neutron counts differ, leading to Carbon-12 having six neutrons and Carbon-13 having seven. Understanding isotopes is essential not just in chemistry, but in fields like archaeology and environmental science as well, where isotope analysis is employed to uncover data ranging from the age of fossils to the sources of pollution.

Neutrons play a critical role in adding nuance to our perception of an element by contributing to the isotopic identity. In an isotope, the neutron count is paramount as it determines the isotope's specific physical properties, such as its atomic mass and stability. To count the neutrons in an isotope, one must know the atomic number, which indicates the number of protons, and subtract this number from the atomic mass number (the sum of protons and neutrons).

The example from our exercise with Carbon-12 and Carbon-13 aptly illustrates this. Both isotopes have an equal atomic number, 6, representing the protons. To find the number of neutrons, subtracting the atomic number from the atomic mass number gives us 6 neutrons in Carbon-12 (12 - 6), and 7 in Carbon-13 (13 - 6), respectively. Notably, even for ions like Carbon-13 with an extra electron ({ }^{13} {C}^{-}), the neutron count remains unchanged, emphasizing that neutrons are isolated from the electrical alterations caused by electron gain or loss.

The concepts of atomic mass and atomic number are cornerstones of atomic structure, providing insights into an element's identity and composition. The atomic number, unique to each element, is the count of protons in an atom's nucleus and essentially defines the element itself. For example, every atom with six protons is a carbon atom, which is reflected by carbon's atomic number of 6.

The atomic mass number, on the other hand, is the sum of protons and neutrons within the nucleus. It generally approximates the atom's actual mass. Since the number of protons is fixed per element, the variance in atomic mass among isotopes is solely due to the difference in neutrons. This number is crucial in solving problems like our textbook exercise, where understanding both the atomic number and atomic mass number leads us to the correct count of neutrons in isotopes of Carbon. This foundational knowledge serves as a building block for more complex concepts in chemistry such as reactions and bonding.