# How To Calculate Average Atomic Mass

##### Atomic Mass Calculator

The average atomic mass can be calculated by multiplying the mass number and Natural abundance of each of the isotopes and then adding them all together. You can convert the percentage abundance by dividing it by 100. Average atomic mass, measured in amu (atomic mass unit), is a characteristic property of elements having various isotopes.

Some elements like Hydrogen have “different versions”; they vary in the number of neutrons or, say mass number. You can quickly determine the average atomic mass of these isotopes. Hydrogen has three isotopes, i.e. Protium, deuterium, and tritium, having 0,1, and 2 neutrons, respectively. Protium or H-1 makes up almost 99.98% of the Hydrogen found on Earth, so practically, Protium is naturally the most abundant isotope.

When we’re figuring out the atomic mass of Hydrogen, we calculate the average atomic mass of all isotopes of Hydrogen. It may sound as hard as grinding stones, but practically it’s a piece of cake if you follow the below-mentioned step-by-step guide.

Learn simplified steps; how to find average atomic mass of isotopes of an element with a simplified formula, definition, and all the key points to remember.

Before you immerse yourself into the more profound concepts of average atomic mass, quickly going through a few terms can prove to be very vital to your learning process by making it easier to grasp the new concepts.

### Natural abundance:

Natural abundance, quite frequently used in chemistry, refers to how abundantly a specific isotope of a given element is found on the Earth, naturally.

### Mass number

The mass number is another common term that generally refers to the sum of protons and neutrons in the nucleus of an atom.

### Atomic Mass

Before you try to grasp the concept of average atomic mass, you must know that Atomic mass is generally described as the total mass of an atom.

## What is the Average Atomic Mass?

Now that you have already grasped the major vital concepts, let’s move on to the actual subject matter, the average atomic mass. The average atomic mass of isotopes is the mass found by adding the mass of each one multiplied by the natural abundance of each one.

Wondering where to use this concept? This is quite a common concept used when dealing with isotopes.

Isotopes are atoms of an element having different mass numbers, and that’s because of the different numbers of neutrons in the nucleus. The number of protons is always the same, though. When that’s the case, we use average atomic mass for various calculations of the element.

For example, the isotopes of Helium, Helium-3 is sparsely found in nature, while Helium-4 is abundantly found in nature. We may rather say that only one in a million Helium atoms is Helium-3; the rest of them are helium-4 atoms. So when we calculate the average atomic mass of these two isotopes, we find out that it’s around four amu, precisely 4.002602 amu.

Similarly, if you want to figure out the average atomic mass of Carbon isotopes, i.e. C-12 and C-13, the percentage abundances are 98.90% and 1.01%, respectively, while the atomic masses are 12.00amu and 13.0033 amu, respectively. This is quite similar to the above-quoted example. Here too, as the natural abundance of C-12 is dominantly way larger than C-13, the average atomic mass of both of them turns out to be somehow very close to 12 amu, i.e. 12.02 amu.

## Definition of Average Atomic Mass:

To be very precise, we may say that the average atomic mass can be defined as the “The Summation of the atomic masses of all isotopes of a given element, each of them multiplied by their natural abundance on the Earth.”

This is quite a simple definition of average atomic mass. Diving inside the concepts a bit deeper, you can figure out the basic concept of average atomic mass. We all know that every element has a fixed number of protons in the nucleus; however, the number of neutrons may vary.

And this variation of the number of neutrons is the critical factor that ends up in a variation of atomic masses of the atoms of the same element. And these different forms of the same element with different atomic masses are called isotopes. Isotopes possess a different subatomic construction and, thus, vary in nature and ultimately application.

## Average Atomic Mass Formula:

Now let’s figure out how to find out the average atomic mass of an element practically. Now that you all know by means of the above piece of information, that average atomic mass is basically calculated by simply adding up all the atomic mass of isotopes after multiplying each of them with their natural abundance on the Earth. Let’s do it using the formula:

### How to Find  Average Atomic Mass

No matter how hard the calculation process sounds, it takes four simple steps to calculate the average atomic mass of isotopes.

### Formula To Calculate Average Atomic Mass:

Average Atomic Mass= M1f1 + M2f2 + M3f3 + M3f3 + … + Mnfn

Where,

• M stands for the atomic mass of the particular isotope of the given element.
• F stands for the natural abundance of the particular isotope of the given element.

Follow the below-mentioned steps one by one.

1. Make sure to have data about The natural abundance of each isotope of the Element beforehand. If you know it already, you’re just a few steps away from calculating it.
2. You’re going to need the natural abundance of each of them in the fractional form, so convert the percentage by dividing it by 100.
3. Next, you can figure out the mass numbers of each of them.
4. Now put the values in the given formula, and solve it to get the results.

Average Atomic Mass= M1f1 + M2f2 + M3f3 + M3f3 + … + Mnfn

Examples

Example 1.

Find the Average atomic mass of hydrogen. If Isotopes 1H and 2H has natural abundance is 99.984% and 0.0156% respectively. Example 2.

Find the Average atomic mass of hydrogen. If Isotopes 12C and 13C has natural abundance is 99.93% and 1.07% respectively.

Example 3.

Find the Average atomic mass of Carbon. If Isotopes 35Cl and 37Cl has natural abundance is75.76% and 24.24% respectively.

## Conclusion:

The steps mentioned earlier are the best-simplified steps to be followed to calculate the average atomic mass of a given element. Elements having different isotopes have different atomic masses for each of the isotopes. So you can quickly figure out the average atomic mass of all of them if you know the mass of each one as well as the natural abundance percentage. Multiply the natural abundance by the mass number, then add them all, and the result is the average atomic mass of the given element.

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