# Difference between Mass Number and atomic mass unit (AMU)

I am struggling to understand the difference between Mass Number and atomic mass unit (AMU). I read several posts on this site but still confused. Mass Number seems like a number (i.e. number of nucleons in nucleus) whereas AMU is in KG. We do we need 2 units? Also, for a given element both of them seem to be very close to each other. For example mass number for a Carbon -12 is 12 and in AMU it is around 12 too. Any reason for this?

• The amu of a nucleus is not a simple count of the nucleons because of the binding energy. C12 being 12 amu is a result of the definition of the amu. – Jon Custer Feb 26 '19 at 17:38
• It is very important that the mass of a nucleus is not the sum of the masses of its parts! – Jasper Feb 26 '19 at 18:01

$$12$$ amu (atomic mass unit) is the mass of one atom of the isotope $$^{12}\rm C$$ exactly (by definition) and $$^{12}\rm C$$ has a mass number of $$12$$.

The mass of an $$^{16}\rm O$$ atom is $$15.9949$$ amu and $$^{16}\rm O$$ has a mass number of $$16$$.

The term nucleon number is now favoured in place of mass number and the nucleon number is the number of nucleons (protons and neutrons) in the nucleus of an atom.

So one quantity is to do with mass (amu) and the other is to do with the number of particles (mass/nucleon number).

The choice of the mass of $$\frac{1}{12} \,^{12}\rm C$$ atom as the unit of mass was to improve accuracy and reproducibility when measuring atomic masses.

Things are complicated by the fact that the mass of and atom is smaller than the sum of the masses of the individual particles which make up an atom - the so called mass defect.

• Transposed the last two digits of O-16: 15.9949 – Bill N Feb 26 '19 at 18:44

The Mass Number is the number of nucleons (protons+nucleons) in a nucleus, so it is a dimensionless magnitude. The atomic mass unit (AMU) however is a mass unit, it measures mass.

1 AMU is defined as the twelfth of the mass of a C12 atom. It was defined this way so that the mass of an atom and its mass number were roughly equal. C12 has 6 protons and 6 neutrons, so you can think of an AMU being the average mass of a proton and a neutron. This is not exactly true, since part of the mass of the nucleons becomes energy that bonds the nucleus together.

Carbon has three isotopes, but C12 is the most common one (98,9 % of carbon is C12), so the mass of carbon is roughly 12 AMU.

• Because both the proton and the neutron has masses a bit bigger than 1 u, it would be better to say that AMU is slighter smaller than their mass. The concept of average totally misses the value. Regarding carbon, there are many more than 3 isotopes, but only 2 are stable. – Bill N Feb 26 '19 at 18:34

You are somewhat sloppy in the question, so I'll try to clarify things a bit.

1. Mass Number: the mass number of an atom is exactly the number of particles (protons and neutrons) that make up its nucleus. It is always a natural number since it is about counting things.
2. Mass expressed in u (short for (u)amu): this is something that can theoretically measured by a weighing scale and can be converted to kg: $$1 \text{ u} \approx 1.661 \cdot 10^{-27}\text{ kg}$$. This number is one twelfth of the mass of one carbon-12 atom, that's how it was defined.

A single proton has a mass of $$1.007 \text{ u}$$, a single neutron is even heavier: $$m_\text{n} \approx 1.008\text{ u}$$. If twelve of them go together to form carbon-12, the resulting atom has less mass than its parts.

The mass number is the number of nucleons as you said . The AMU is a unit that helps us to communicate weight of atoms in a better manner.

eg) The mass of oxygen-16 atom is $$2.65\times 10^{-26}$$ kg. Now who would remember such an absurd quantity? Hence we define 1 AMU as 1/12th the mass of C-12 atom.

Now instead of $$2.65 \times 10^{-26}$$ we could just say mass of oxygen-16 is approximately 16 amu.