Relative Isotopic Mass: The Atomic Weight Scale
What is an Isotope and Why Do We Need a Scale?
Atoms are the tiny building blocks of everything you see around you. Every atom is made up of a nucleus containing protons and neutrons, with electrons whizzing around it. The number of protons defines which element an atom is. For example, any atom with 6 protons is a carbon atom, and any atom with 1 proton is a hydrogen atom.
However, not all atoms of the same element are identical. They can have different numbers of neutrons in their nucleus. These different forms of the same element are called isotopes[1]. Because neutrons have mass, different isotopes of the same element have different masses.
This is where it gets tricky. The actual mass of a single proton or neutron is incredibly small. For example, the mass of a proton is about $1.67 \times 10^{-27}$ kg. Working with such tiny numbers is very inconvenient for calculations. Scientists needed a simpler way to talk about and compare the masses of atoms and their particles. The solution was to create a relative scale—a way to compare atomic masses to a common, agreed-upon standard.
The Carbon-12 Standard and the Atomic Mass Unit
The international scientific community chose one specific isotope to act as this standard: carbon-12. A carbon-12 atom has 6 protons and 6 neutrons in its nucleus.
This definition is the cornerstone of the concept. By setting the mass of carbon-12 to exactly 12 atomic mass units, we create a fixed scale. Now, the mass of any other atom or isotope can be expressed relative to this scale. This relative mass is what we call the relative isotopic mass.
So, if a hydrogen-1 atom (which has 1 proton and 0 neutrons) is found to have a mass that is approximately 1/12 that of a carbon-12 atom, its relative isotopic mass is approximately 1. This makes calculations and comparisons much more straightforward.
A Closer Look at Isotopes and Their Masses
Let's explore some common isotopes to see how this works in practice. The relative isotopic mass is not usually a whole number, even though the number of protons and neutrons are whole numbers. This is because the mass of a neutron is slightly more than the mass of a proton, and there is also a small amount of mass converted into energy that holds the nucleus together (this is called binding energy).
| Element | Isotope Symbol | Protons | Neutrons | Relative Isotopic Mass (approx.) |
|---|---|---|---|---|
| Hydrogen | $^{1}_{1}H$ | 1 | 0 | 1.0078 |
| Hydrogen | $^{2}_{1}H$ (Deuterium) | 1 | 1 | 2.0141 |
| Carbon | $^{12}_{6}C$ | 6 | 6 | 12.0000 (by definition) |
| Carbon | $^{13}_{6}C$ | 6 | 7 | 13.0034 |
| Chlorine | $^{35}_{17}Cl$ | 17 | 18 | 34.9689 |
| Chlorine | $^{37}_{17}Cl$ | 17 | 20 | 36.9659 |
Notice from the table that the relative isotopic mass is very close to the mass number (protons + neutrons), but it is not exactly the same. For instance, chlorine-35 has a mass number of 35, but its precise relative isotopic mass is 34.9689. This small difference is significant in precise chemical calculations.
How to Calculate Relative Isotopic Mass
The relative isotopic mass is determined experimentally using an instrument called a mass spectrometer. This device can separate different isotopes of an element based on their mass-to-charge ratio and measure their individual masses with high precision relative to the carbon-12 standard.
While we don't calculate it from first principles in a classroom, we can understand the concept through a simple thought experiment. Imagine you have a very precise balance scale. On one side, you place exactly 12 atoms of carbon-12. On the other side, you place atoms of another isotope, say oxygen-16. You would find that you need 16 atoms of oxygen-16 to balance the scale. Therefore, the relative isotopic mass of oxygen-16 is 16.
In reality, as we saw with chlorine, the masses are not perfect whole numbers. The calculation is more complex and involves comparing the mass of the isotope to 1/12th the mass of a carbon-12 atom directly.
Applying the Concept: From Isotopes to Elements
Most elements exist naturally as a mixture of isotopes. For example, chlorine is found as about 75% chlorine-35 and 25% chlorine-37. This is why the atomic mass of chlorine you see on the periodic table is 35.45, not a whole number. This value is the relative atomic mass[2], which is the weighted average of the relative isotopic masses of all the naturally occurring isotopes of an element.
Let's calculate the relative atomic mass of chlorine using the data from our table:
- Relative Isotopic Mass of Cl-35 = 34.9689, Abundance = 75.77%
- Relative Isotopic Mass of Cl-37 = 36.9659, Abundance = 24.23%
The calculation is a weighted average:
$(34.9689 \times 0.7577) + (36.9659 \times 0.2423) = 35.45$
This example shows how the concept of relative isotopic mass is the foundational building block for understanding the atomic masses we use every day from the periodic table. Without knowing the individual masses of the isotopes, we could not calculate the average mass for the element.
Common Mistakes and Important Questions
Q: Is relative isotopic mass the same as the mass number?
Q: Why was carbon-12 chosen as the standard? Why not oxygen-16 or hydrogen-1?
Q: What is the difference between relative isotopic mass and relative atomic mass?
Footnote
[1] Isotope: Different forms of the same element that have the same number of protons but different numbers of neutrons. They have identical chemical properties but different physical masses.
[2] Relative Atomic Mass (Ar): The weighted mean mass of an atom of an element relative to 1/12 of the mass of an atom of carbon-12. It is the number you see for each element on the periodic table.