The atomic mass of an element can also be calculated based on the isotopic abundances of its naturally occurring isotopes. The formula for calculating atomic mass using isotopic abundances is as follows:
Atomic mass = (Mass of Isotope 1 * Abundance of Isotope 1) + (Mass of Isotope 2 * Abundance of Isotope 2) + … + (Mass of Isotope n * Abundance of Isotope n)
In this formula, the mass of each isotope is multiplied by its corresponding abundance (expressed as a decimal or percentage), and the products are summed to obtain the atomic mass. This accounts for the relative proportions of each isotope in a naturally occurring sample of the element.
Let’s take the element chlorine (Cl) as an example.
Chlorine has two naturally occurring isotopes: chlorine-35 (mass = 34.9689 atomic mass units) and chlorine-37 (mass = 36.9659 atomic mass units). The abundances of these isotopes are approximately 75.77% and 24.23% respectively.
To calculate the atomic mass of chlorine using the isotopic abundances, we can use the formula:
Atomic mass = (Mass of chlorine-35 * Abundance of chlorine-35) + (Mass of chlorine-37 * Abundance of chlorine-37)
Plugging in the values:
Atomic mass = (34.9689 amu * 0.7577) + (36.9659 amu * 0.2423)
Calculating the expression:
Atomic mass ≈ 26.4984 amu + 8.9623 amu ≈ 35.4607 amu
So, the atomic mass of chlorine, based on the isotopic abundances, is approximately 35.4607 atomic mass units.
The atomic mass of an element is calculated by summing the masses of its protons and neutrons in the nucleus. The formula for calculating atomic mass is as follows:
Atomic Mass = (Mass of Protons * Number of Protons) + (Mass of Neutrons * Number of Neutrons)
In this formula, the mass of protons and neutrons is given in atomic mass units (u), and the number of protons and neutrons is the respective count for the specific element.
