Atomic masses and the nucleus

Weighing atoms

Narrated video. Transcript:

Blow an atom up to the size of your classroom. The nucleus at its centre would be about the size of a pinhead. Yet that pinhead holds more than 99.9 per cent of the mass of the atom.

Atoms are very light. One carbon-12 atom has a mass of 1.992647 × 10⁻²⁶ kilogram. The kilogram is far too big a unit for such tiny masses.

So we use the atomic mass unit, u. One u is one-twelfth of the mass of a carbon-12 atom. Divide by 12, and 1 u equals 1.660539 × 10⁻²⁷ kilogram.

Atomic masses are measured very accurately with a mass spectrometer. Most come out close to whole-number multiples of the mass of a hydrogen atom. But chlorine is 35.46 u. Why the odd half?

Because chlorine is a mixture. The spectrometer finds two kinds of chlorine atom, of masses 34.98 u and 36.98 u. Same element, same chemistry, different masses. These are called isotopes, from the Greek for same place in the periodic table.

In natural chlorine, 75.4 per cent of the atoms are the lighter kind and 24.6 per cent the heavier. The average is 75.4 × 34.98 plus 24.6 × 36.98, all over 100.

That works out to 35.47 u, which matches the measured atomic mass of chlorine. So an atomic mass is a weighted average over the isotopes.

Even hydrogen has three isotopes, of masses 1.0078 u, 2.0141 u and 3.0160 u. The lightest, ordinary hydrogen, makes up 99.985 per cent of all hydrogen.

Its nucleus is the proton. Take the hydrogen atom, 1.00783 u, and remove its electron, 0.00055 u. The proton’s mass is 1.00727 u, or 1.67262 × 10⁻²⁷ kilogram.

A proton carries one unit of positive charge, plus e. A neutral atom has Z electrons outside its nucleus, so its nucleus has charge plus Ze, and holds exactly Z protons.

Protons, neutrons and nuclides

Narrated video. Transcript:

Hydrogen, deuterium and tritium all have one proton, since they are the same element. Yet their nuclei have masses in the ratio 1 : 2 : 3. So something neutral must add the extra mass.

In 1932, James Chadwick fired alpha particles at beryllium. Out came a neutral radiation that could knock protons out of light nuclei like helium, carbon and nitrogen.

If this radiation were photons, they would need far more energy than the reaction could give. Using conservation of energy and momentum, Chadwick showed it was a new neutral particle, almost as heavy as a proton: the neutron.

The neutron’s mass is 1.00866 u. A free neutron is unstable: in about 1000 seconds it decays into a proton, an electron and an antineutrino. Inside a nucleus it is stable.

Now we can describe any nucleus with three numbers. Z, the atomic number, is the number of protons. N, the neutron number, is the number of neutrons. A, the mass number, is Z plus N.

Protons and neutrons together are called nucleons, so A is the number of nucleons. A nuclear species, or nuclide, is written as the symbol X with A at the top left and Z at the bottom left.

For example, gold is ¹⁹⁷₇₉Au. It has 197 nucleons. 79 are protons, so 197 minus 79, that is 118, are neutrons.

Isotopes have the same Z but a different N. Deuterium, ²₁H, has one proton and one neutron; tritium, ³₁H, has one proton and two neutrons. Gold has 32 isotopes, from A equals 173 to 204.

Nuclides with the same mass number A are isobars, like ³₁H and ³₂He. Nuclides with the same neutron number N are isotones, like ¹⁹⁸₈₀Hg and ¹⁹⁷₇₉Au, which both have 118 neutrons.

An easy way to remember: isotoPes keep P, the protons; isobArs keep A; isotoNes keep N.

Try it: build a nucleus

Interactive simulation. Things to try:

• Add one neutron to carbon-12: the element stays carbon, A becomes 13, and it is still stable. Add two more and it becomes unstable.
• Add a proton instead: the element changes. Z alone decides which element it is.
• Switch between isotopes, isobars and isotones: the family is a row, a diagonal or a column of the chart.
• Look at the shaded stable squares. For light nuclei they sit near N = Z; by calcium they drift towards more neutrons.
• Tap any square on the chart to jump to that nuclide.

Spot the isotones

Which pair of nuclides are isotones?

1. ¹²₆C and ¹⁴₆C
2. ¹⁴₆C and ¹⁴₇N
3. ¹³₆C and ¹⁴₇N
4. ¹⁶₈O and ¹⁸₈O

The mass of boron

Boron has two isotopes: ¹⁰B of mass 10.0129 u (19.9 %) and ¹¹B of mass 11.0093 u (80.1 %). What is the atomic mass of boron?

1. 10.51 u
2. 10.21 u
3. 10.81 u
4. 11.01 u

Summary

• Atomic mass unit: 1 u = (mass of one ¹²C atom)/12 = 1.660539 × 10⁻²⁷ kg
• Nucleon masses: m_p = 1.00727 u, m_n = 1.00866 u
• Mass number: A = Z + N
• Nuclide: ᴬ_Z X, e.g. ¹⁹⁷₇₉Au: 79 protons, 118 neutrons

• The nucleus is about 10⁴ times smaller than the atom but holds more than 99.9 % of its mass.
• A nucleus has Z protons (charge +Ze) and N neutrons. The neutron, found by Chadwick in 1932, is neutral and almost as heavy as a proton.
• Isotopes: same Z, different N (same chemistry). Isobars: same A. Isotones: same N.
• The atomic mass of an element is the weighted average of its isotopes’ masses, e.g. chlorine: 35.47 u.