# How to calculate atomic mass

Everything we know is built of the same basic particles that combine in different amounts inside entities called atoms. A small change, for example, in the number of protons that form an atom’s nucleus may alter its properties altogether.

All the elements and some of their characteristics depend on the specific combination of these subatomic particles. But, when studying this topic, you might stumble into a confusing bowl of jargon.

Molecular weight, molar mass, atomic weight, and atomic mass are all different concepts which tend to be mixed up. The last one of these, the atomic mass, refers to the total mass contained in a specific type of atom. While mass is most usually measured in kilograms, atomic mass is measured using a special unit called Dalton. Let’s briefly review this concept and learn how to master it!

## How to calculate the atomic mass of an atom

A specific isotope’s atomic mass corresponds to its total mass expressed in Dalton (u), also called unified atomic mass units. It is obtained by dividing the mass of the isotope (M) in kilograms by the equivalent of 1 u, namely 1,66 x 10^-27kg:

Where m is the atomic mass in Dalton.

## What is the atomic mass?

Atoms form all the objects you see around you. These entities come together to build molecules, which constitute the air we breathe, the chair you are probably sitting on, and the screen you are using to read this.

Nevertheless, these basic units are made of even smaller entities called subatomic particles, such as protons, neutrons, and electrons. The first two build up the nucleus, while the last ones inhabit the space around it, inside the so-called electron “cloud”. The atom’s structure is usually represented like this:

The previous picture might be misleading, especially because it does not keep the right proportions. If a whole atom were a few kilometers in size, its nucleus would only be around the size of a tennis ball. However, this tiny section actually possesses most of the atom’s mass. This is due to the fact that electrons are around 1800 times lighter than protons or neutrons, as you can see in the following table:

Protons are positively charged particles, while electrons are negatively charged. The amount of charge each of them possesses is the same but opposite, namely, 1.06 x 10^-19 coulombs. This means that one proton together with one electron would form an electrically neutral entity, since both charges would cancel.

An atom with a given number of protons in its nucleus will always try to have the same number of electrons in its electron cloud in order to remain neutral. This is precisely what happens when you shake hands with someone and feel an electric shock:

The atoms in your or the other person’s hand have lost electrons, probably due to friction with other surfaces. Since the number of protons in them is now greater than that of electrons, those atoms are positively charged.  When both hands come together, the positively charged atoms will steal the missing number of electrons from other neutral or negatively charged atoms nearby, thus creating an electron flow through space. This is what we call an electric current

Now, altering the number of electrons inside an atom is relatively simple. This is because the energy binding them to the nucleus can be easily surpassed by friction, heat, electric fields, and many other types of stimuli. On the contrary, the number of protons that builds up the nucleus is more stable, given that the energy keeping them together, called the strong nuclear force, is extremely high. Only during a nuclear reaction or by radioactive decay will this number change. Go ahead and read more about how to calculate an element’s half-life to learn more about this interesting phenomenon!

The number of protons inside an atom’s nucleus determines the type of element that is built. For example, a hydrogen atom consists of one proton, while a uranium atom consists of 92! Every element on the periodic table has a unique number of protons, which is called the atomic number (Z). The following table shows the elements corresponding to the first 10 atomic numbers and their chemical symbols:

While the number of protons inside an atom’s nucleus remains constant for a certain element, the number of neutrons can change. This builds the different isotopes of every element. Coming from the Greek “iso”, which means equal, and “topos”, which means place, isotopes are variations of the same element, which might have slightly different properties.

For example, a hydrogen atom with only one proton in its nucleus (hydrogen-1) is called protium, while an atom with one proton and one neutron (hydrogen-2) is called deuterium. The different isotopes of hydrogen can occur naturally, although hydrogen-1 accounts for 99,98% of all hydrogen on Earth, while hydrogen-2 only for 0,0156%. The total number of protons and neutrons present in the nucleus of an atom is called its mass number. So, protium and deuterium have mass numbers of 1 and 2, respectively.

Now, the total mass of a specific atom equals the sum of the masses of the individual subatomic particles contained in it. This is called the atomic mass. Naturally, different elements will have different atomic masses, since the number of protons in their nuclei differ from each other. Furthermore, atoms of the same element might have different atomic masses depending on the specific isotope. Let’s use hydrogen as an example:

As we mentioned before, protium consists of only one proton and no neutrons. This means, its total atomic mass is:

On the other hand, deuterium atoms consist of one proton and one neutron, yielding a total atomic mass of:

Keep in mind we do not take the masses of the electrons into account, since it is so mall that the difference in the result is negligeable. The following image illustrates the previous example:

So, in summary, the atomic mass refers to the total mass of a specific type of isotope. Nevertheless, using kilograms to express such a small number might be tricky, and scientific notation is usually required. For this reason, scientists use Daltons instead, which are also called the unified atomic mass units, denoted as Da or u.

One Dalton is defined as 1/12 of the mass of an unbound neutral atom of carbon-12 at rest, which is 1,99 x 10^-26 kg. So, by definition, the equivalency between Daltons and kilograms is:

Using this definition, a carbon-12 atom would have an atomic mass of 12 u, while protium and deuterium atoms would have masses of 1,0076 u and 2,0166 u, respectively.

Keep in mind that most periodic tables show elements’ atomic weight, which can differ from the atomic mass. This concept refers to the weighted average of the atomic masses of the different isotopes of a specific element, where the weights used for the calculation are the percentages in which each isotope is present in a given sample. On the other hand, the atomic mass refers to a single isotope’s mass. Keep in mind the atomic mass should also not be confused with the molar mass

## How to convert atomic mass in Daltons to kilograms?

Most sources use Daltons to express atomic masses. To convert these values into kilograms, we can simply use a cross multiplication. Using equation 4, we can write:

Where m is the atomic mass of the atom in Dalton, while M is its atomic mass in kilograms. Solving this equation for M, we get:

Using equation 6 you can calculate any atom’s atomic mass in kilograms based on its value in Daltons. Conversely, if you know the atomic mass in kilograms, you may convert it to Dalton simply by using equation 1 —which results from rearranging equation 6—. Let’s look at one example:

An oxygen-16 atom has an atomic mass of 15,9949 u. Its mass in kilograms is then:

To confirm this result, you can calculate the total mass in the atom’s nucleus by adding that of the 8 protons and 8 neutrons present in it. Go ahead and do the math!

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