Describe the two different notations used to specify isotopes and give an example of each.

Understanding the hyphen notation in the context of isotopes is quite straightforward. It involves the element's name followed by a hyphen and the mass number, which represents the sum of protons and neutrons in the nucleus of the atom. For instance, when we look at Carbon-14, we're dealing with the element carbon (C) and its isotope that has a mass number of 14. This means, since the carbon atom always has 6 protons, Carbon-14 must have 8 neutrons because 6 (protons) + 8 (neutrons) = 14 (mass number).
Hyphen notation is commonly used in various scientific fields, as it effectively distinguishes between different isotopes of an element simply by showcasing the mass number.

Another way to write isotopes is using the nuclear symbol notation. This method displays the isotope with the chemical symbol of the element, the atomic number as a subscript, and the mass number as a superscript to the left of the symbol. For instance, the nuclear symbol notation for Carbon-14 would be written as \( {}^{14}_{6}\text{C} \). Here, the 6 (written as a subscript) represents the atomic number, which is also the number of protons in carbon, while 14 (written as a superscript) represents the mass number. This format is particularly useful for chemists and physicists as it provides an immediate understanding of the isotope's composition without spelling out the element's full name.

The mass number plays a critical role in distinguishing between isotopes. It is denoted by the sum of an atom's protons and neutrons, which are collectively known as nucleons. The mass number is significant because while the number of protons (atomic number) defines the type of element, the number of neutrons can vary, resulting in different isotopes of the same element. Thus, the mass number is integral in specifying these isotopes. In isotopes with a higher mass number, there are simply more neutrons present than in those with a lower mass number. However, it's essential to note that the mass number is always a whole number as it counts the number of particles.

At the heart of chemical elements lies the atomic number. This integer is the number of protons found in the nucleus of an atom and is fundamental to an element's identity. Every atom of the same element has the same atomic number, which is why it's represented as a subscript in the nuclear symbol notation. For example, all carbon atoms have an atomic number of 6, denoted as \( {}_{6}\text{C} \) in nuclear symbol notation. This number not only defines the element but also determines its position within the periodic table. Unlike the mass number, the atomic number does not change among isotopes of the same element; what differentiates the isotopes is the number of neutrons.