# Atomic Weight

by Ron Kurtus (updated 8 February 2022)

Since the actual weight of an atom is extremely small, a more convenient way of designating the relative mass of the various atoms is the * atomic weight*.

The atomic weight of an atom was originally defined as the sum of the number of its protons and its neutrons. Unfortunately, this idea proved not valid as exact measurements of the actual weights of the various elements and sub-atomic particles were made.

The new definition of an atomic mass unit is that it is 1/12 of the atomic weight of Carbon-12. Most listing of elements include isotopes to display an average atomic weight.

Questions you may have include:

- What was the original atomic weight concept?
- What is the new definition of atomic weight unit?
- How do isotopes skew the atomic weight?

This lesson will answer those questions. Useful tool: Units Conversion

## Original atomic weight

Originally, the atomic weight of an atom was defined as the sum of the number of its protons and neutrons. It was assumed that protons and neutrons had the same mass, so each proton and neutron was given the atomic weight of 1. The weight of electrons were considered negligible and did not contribute enough to the total atomic weight to count. Thus, the actual weight of any atom would be a multiple of the actual weight of a Hydrogen atom.

## Element |
## Atomic Number |
## Neutrons |
## Original |

Hydrogen |
1 | 0 | 1 |

Helium |
2 | 2 | 4 |

Oxygen |
8 | 8 | 16 |

Iron |
26 | 30 | 56 |

Uranium |
92 | 146 | 238 |

Original Atomic Number Scheme

Unfortunately, improved measurements showed that the mass or weight of most atoms was not exactly the sum of the protons and neutrons.

### Protons and neutrons not equal

One reason for the mass difference is that it was found that neutrons were slightly heavier than protons.

The actual mass of these particles is:

- Proton: 1.6726*10
^{-27}kg - Neutron:1.6749*10
^{-27}kg - Electron 0.0009*10
^{-27}kg

where 10^{-27} = 1/10^{27}, and 10^{27} is 1 followed by 27 zeros.

### Mass defect

Another factor that explained why the weight was different is that nuclear binding effects changed the mass of a nucleus.

Since protons have a positive charge, they should repel each other. But within a nucleus, there is a binding force that holds the protons together, along with the electrically-neutral neutrons. As the atomic weight increases, there is greater potential energy built up in the nucleus.When the protons and neutrons combine to form a nucleus, some mass is lost in the binding process. This "lost" mass is called the *mass defect* of the nucleus. This mass defect is the principle of nuclear energy, according to Einstein's famous equation:

E = mc²

where **m** is the mass defect mass and **c** is the speed of light.

## New definition

The definition of atomic weight has gone through numerous changes that may be somewhat confusing and illogical.

### Unit equals 1/12 Carbon-12 atomic weight

The unit of atomic weight is presently also called *atomic mass unit* (**amu**), *unified atomic mass unit* (**u**) and *Dalton* (**Da**). Different scientific organizations want their own nomenclature, thus making things confusing. Although you may run into different terminologies, we'll avoid the argument and continue calling it atomic weight.

The unit of atomic weight is also called *atomic mass unit* (**amu**). Setting Carbon-12 as having an atomic weight of 12, the atomic mass unit is defined as 1/12 the atomic weight of Carbon-12.

Since the actual mass of Carbon-12 is about 19.9*10^{-27 }kg, 1 amu = 1.66*10^{-27 }kg.

### Proton not 1

Although one would think they would simply leave the proton as 1 and adjust the atomic weight of the neutron, some convoluted logic was used to change the atomic weights to:

- Proton: 1.0073 amu
- Neutron: 1.0087 amu
- Electron: 0.0005 amu

What started to be a simple system using integers has turned into something more complex.

## Average atomic weight

But wait, there still are more changes.

### Isotopes added in

An element consists of several isotopes, each with the same atomic number or number of protons, but with different numbers of neutrons. Usually one isotope is common and the others consist of a small percentage of the total.

Listings of atomic weights or unified atomic mass units usually average the isotopes of an element. Thus, even if the old integer system for atomic weights held, the number still wouldn't be simple. For example, the atomic weight of Carbon-12 is 12 amu. But Carbon consists of C-12, C-13, and C-14 isotopes. Thus the average atomic weight of Carbon is 12.01 amu.

(See *Isotopes* and *The Elements* in the **Chemistry** section for more information.)

### Finding number of neutrons

You still can find the number of neutrons for an element by its average atomic weight. You take the atomic weight and round it off to become an integer or whole number. Then you subtract the atomic number (and thus the number of protons) to get the number of neutrons.

The atomic weight of Carbon is 12.01. That rounds off to 12. The atomic number of Carbon is 6. Thus, the number of neutrons is 12 - 6 = 6.

But note that this only holds for the *most common isotope* of the element. In this case, it only holds for Carbon-12.

## Summary

The atomic weight or mass of an element is approximately the sum of the number of protons and neutrons in the nucleus. This value is not a whole number because the atomic weights of the proton and neutron are not exactly 1, the additional effect of energy-mass factor of fission and fusion reactions, and the averaging of the weights of isotopes. The fact that the atomic weights are not the whole numbers as originally planned has brought about some confusion.

Science can be amazing

## Resources and references

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atomic_weight.htm**

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## Where are you now?

## Atomic Weight