## Why is the Mass Number on the Periodic Table Not a Whole Number?

When you started to study A-Level or Advanced Higher chemistry you will have noticed a few changes on the periodic table you now use.

One of those changes is that the mass number is no longer a whole number. The periodic table you used previously had a whole number for most elements, such as the example snippet below.

Well, there are two reasons why you now see decimal numbers on your periodic table.

The first reason is that the number on the periodic table that you use now is the relative atomic mass (R.A.M. or Ar), not the mass number.

And the second reason is the existence of isotopes.

Let’s deal with those one at a time.

### Mass Number or Relative Atomic Mass?

I mentioned above that the basic periodic table shows the mass number rather than the relative atomic mass. The mass number is a simple count of the total number of protons and neutrons of a typical atom of the element, and that’s why it is a whole number. (We will talk about the exception of chlorine later in this article).

The R.A.M. is the actual mass. As you would expect, the mass of an individual atom is tiny and it would be impractical to use the grams for their mass.

So you’ll probably recall that we use atomic mass units (a.m.u.). And you may remember that we define one a.m.u. as being exactly 1/12th the mass of a 12C atom.

The mass of atoms of each other element is compared to the mass of that 12C atom. For example, the mass of a typical lithium atom is 6.9 a.m.u.. That means a lithium atom weighs 6.9 x 1/12th the mass of a 12C atom.

It’s the same for all other elements. The R.A.M. shown on the periodic table for any element is based upon it’s mass relative to that of a 12C atom.

We will consider relative atomic mass in more detail and explain how we can use it in a future article and podcast episode.

### Isotopes and Their Influence on R.A.M.

Isotopes are variants of atoms of the same element. The difference between them is their mass number, and consequently their mass.

Because all atoms of a particular element must have the same number of protons, they differ in the number of neutrons in their nuclei.

Does this affect the way that different isotopes behave? The atoms of different isotopes of an element have exactly the same behaviour in all chemical reactions. However, some isotopes display radioactive behaviour whilst many don’t.

In summary, isotopes of an element:

• have the same number of protons to each other
• have a slightly different number of neutrons to each other
• have a slightly different mass to each other
• have identical chemical properties – with the exception that some isotopes display radioactive behaviour

In order to see the affect on relative atomic mass, and to be able to calculate this, we need to know the relative abundance of the stable isotopes of an element.

### What is Relative Abundance?

Relative abundance is the proportion of a naturally occurring sample of an element comprised of atoms of a particular isotope, and is usually expressed as a percentage of the atoms in the sample. The relative abundances of all the isotopes add up to 100%.

This can be measured using mass spectrometry.

## How to Calculate (Relative) Atomic Mass

It may seem a complicated name but relative atomic mass is simply the average atomic mass of the atoms of a particular element.

The calculation takes into account the relative abundance and mass of the isotopes.

We can calculate the mass using this mathematical equation:

Ar is the average atomic mass for the element (R.A.M.)

Σ (mass x relative abundance) means the sum of isotope mass x the isotope’s relative abundance (%).

The right hand side is divided by 100 because we express relative abundance as a percent.

We do have a walkthrough of an example (from a real exam question) in the mass spectrometry course available for you as a member of our membership program.

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