The unified atomic mass unit

7 minAS Level11.1.12

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can define the unified atomic mass unit, state its value in kilograms, and convert a mass given in u into kilograms and back.

Definition

Unified atomic mass unit (u)

One unified atomic mass unit is defined as exactly $\dfrac{1}{12}$ of the mass of a carbon-12 atom:

$1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg}$

The definition includes the atom's electrons, but a carbon-12 atom's electrons contribute only about 0.03% of its mass, so for nuclear purposes $1\ \text{u}$ is essentially the mass of one nucleon.

Why a new unit is needed

A proton's mass is $1.7 \times 10^{-27}\ \text{kg}$ . Writing that out for every particle, and comparing the mass of a nucleus with the masses of the particles that make it, would mean juggling very small powers of ten. The atomic mass unit removes most of that work:

particle	mass in u	mass in kg
proton	1.007	$1.67 \times 10^{-27}$
neutron	1.009	$1.67 \times 10^{-27}$
electron	0.00055	$9.1 \times 10^{-31}$
alpha particle	4.002	$6.64 \times 10^{-27}$

Nuclei then have masses that are close to their nucleon numbers: a $^{235}_{92}\text{U}$ nucleus is quoted as about $235\ \text{u}$ rather than $3.9 \times 10^{-25}\ \text{kg}$ . That is why $A$ is called the mass number — it is the mass in u, to within a fraction of a percent.

To convert:

$\text{mass in kg} = \text{mass in u} \times 1.66 \times 10^{-27}\ \text{kg}$

and divide instead of multiplying to go the other way.

Close to 1, but never exactly 1

A nucleon has a mass slightly more than $1\ \text{u}$ — a proton is $1.007\ \text{u}$ and a neutron $1.009\ \text{u}$ — while a nucleus of nucleon number $A$ has a mass slightly less than $A\ \text{u}$ .

The reason is that when nucleons bind together, a small amount of mass is converted into binding energy: the mass defect. Adding up two protons and two neutrons separately gives about $2(1.007) + 2(1.009) = 4.032\ \text{u}$ , while a helium-4 nucleus has a mass of $4.002\ \text{u}$ : the missing $0.030\ \text{u}$ became binding energy. For the same reason a uranium-235 nucleus is not exactly $235\ \text{u}$ .

For the purposes of this topic the difference is small enough to ignore; in the A2 work on mass defect it becomes the whole point.

Worked example: Converting an alpha particle's mass

An alpha particle has a mass of $4.002\ \text{u}$ . Express this in kilograms, and state why the value is close to that of four nucleons.

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Multiple choiceQuestion 1 · Recall

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