8867 / 2027
Nuclear Physics overview

Lesson 2 of 9

Count atoms, nuclei and nucleons

  • I can state and use the Avogadro constant to count specified entities in a mole or sample.Syllabus

    Syllabus 8867, 11(d). State and use the Avogadro constant to count specified entities in a mole or sample.

Make a guess. You are not marked.

About how many atoms are in 1.0 g of carbon-12?

  1. About 5.0 x 1022, one twelfth of a mole.
  2. About 7.2 x 1024, multiplying the Avogadro constant by 12.
  3. About 6.0 x 1023, because that is the Avogadro constant.
Show the answer

About 5.0 x 1022, one twelfth of a mole.

12 g of carbon-12 is one mole, 6.02 x 1023 atoms. 1.0 g is one twelfth of that: 5.0 x 1022 atoms.

The mole counts specified entities. Calculate the number of atoms or molecules first, then use their composition to count nuclei, protons, neutrons or electrons.

One mole contains 6.02 × 1023 entities. With amount of substance n, sample mass m, molar mass M and Avogadro constant NA:

n = m/M
N = nNA
NA = 6.02 × 1023 mol-1

Use matching mass units: g with g/mol, or kg with kg/mol. N counts the entity named by the molar mass. It is not automatically the count of every nucleus or nucleon within a molecule.

Separate relative mass from mass and molar mass

Relative atomic mass Ar is the mean atomic mass relative to one twelfth of the mass of a neutral carbon-12 atom. Relative molecular mass Mr is the corresponding ratio for a molecule. Both are dimensionless.

An individual atomic mass ma has a unit such as kg or u; molar mass M has a unit such as kg/mol or g/mol. The familiar numerical correspondence between relative mass and molar mass in g/mol is sufficient for the rounded supplied examples, but it does not give Ar or Mr a g/mol unit.

Worked argon sample

One nucleus per atom, forty nucleons per nucleus

A few times 10-4 mol should contain order 1020 entities. Now take 0.0200 g of pure neutral argon-40, with supplied M = 40.0 g/mol:

n = 0.0200/40.0 = 5.00 × 10-4 mol
N = (5.00 × 10-4)(6.02 × 1023)
= 3.01 × 1020 atoms or nuclei

The same calculation uses 2.00 × 10-5 kg and 0.0400 kg/mol. Each argon-40 nucleus contains 18 protons and 22 neutrons:

Particle counts in the supplied argon-40 sample
EntityCalculationSample count
Protons18N5.418 × 1021
Neutrons22N6.622 × 1021
Electrons18N5.418 × 1021
Nucleons40N1.204 × 1022

The electron count uses the stated neutrality. At three significant figures, the proton and neutron totals are 5.42 × 1021 and 6.62 × 1021. Use the supplied molar mass rather than treating mass number 40 as an exact molar-mass measurement.

This stable-isotope counting example is separate from the radioactive models later in the chapter.

A molecule can contain several nuclei

For H2O, supplied Ar(H) = 1.0 and Ar(O) = 16.0 give Mr = 2(1.0) + 16.0 = 18.0, without a unit. Using supplied M = 18.0 g/mol, a 1.80 g sample contains:

n = 1.80/18.0 = 0.100 mol
Nmolecules = 6.02 × 1022
Nnuclei = 3Nmolecules = 1.806 × 1023

There are three atomic nuclei in each molecule. The molecule count and nucleus count therefore differ even though they describe the same sample.

Check your understanding

A 0.0200 g sample of pure argon-40 has supplied molar mass 40.0 g/mol. With N_A = 6.02 x 1023 mol-1, how many argon nuclei does it contain?

  1. 5.00 x 10-4 nuclei.
  2. 3.01 x 1020 nuclei.
  3. About 1.20 x 1022 nuclei.
Show the answer

3.01 x 1020 nuclei.

n = m/M = 5.00 x 10-4 mol, so N = nN_A = 3.01 x 1020 atoms. Each atom contains one nucleus; its 40 nucleons are a different count.