Why are the atomic masses of elements usually decimal numbers?
Atomic masses are average masses of the different isotopes of that element that occur naturally. For example, the mass of Cl-35 and the mass of Cl-37 are averaged (about 76% for 35 and 24% for 37) and the weighted average is about 35.5 for naturally occurring Cl2.
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The atomic masses of elements are usually decimal numbers because they are the weighted averages of the masses of all naturally occurring isotopes of that element. Isotopes are variants of an element that have the same number of protons but differ in the number of neutrons. Since different isotopes have slightly different masses, the atomic mass takes into account the relative abundance of each isotope and calculates a weighted average.
To determine the atomic mass of an element, you can follow these steps:
1. Identify the naturally occurring isotopes of the element: Find a reliable source, such as a periodic table or a scientific database, that lists the isotopes of the element and their respective abundances.
2. Determine the mass of each isotope: Look up the atomic mass of each isotope. It represents the sum of the masses of all the protons, neutrons, and electrons in the atom.
3. Calculate the weighted average: Multiply the mass of each isotope by its abundance, expressed as a decimal or a percentage. Then, sum up these values to obtain the atomic mass.
For example, let's calculate the atomic mass of carbon:
Carbon has two naturally occurring isotopes: carbon-12 (98.93% abundance) and carbon-13 (1.07% abundance). The atomic masses of these isotopes are approximately 12 and 13 amu, respectively.
To calculate the atomic mass of carbon:
(12 amu * 0.9893) + (13 amu * 0.0107) = 12.01 amu
Therefore, the atomic mass of carbon is approximately 12.01 atomic mass units (amu).
It's important to note that atomic masses are usually expressed as decimal numbers to reflect the fact that they are the weighted average of isotopes. In some cases, atomic masses may be whole numbers if an element has only one stable isotope or if the atomic masses of the isotopes happen to be very close to whole numbers.