Atoms, isotopes and relative atomic mass

Protons, neutrons and electrons, nuclide notation for atoms and ions, isotopes and their properties, mass spectra, and calculating relative atomic mass and isotopic abundance.

The data sheet gives chlorine a relative atomic mass of 35.45. Yet no chlorine atom anywhere has a mass of 35.45. About three quarters of chlorine atoms have a mass close to 35, and the rest close to 37. The 35.45 is an average, weighted by how common each kind is. Working out where that number comes from is the first job of this lesson.

Inside the atom

By 1932 experiments had shown that atoms contain three kinds of particle. Protons and neutrons, together called nucleons, sit in a tiny dense nucleus; electrons occupy the space around it. The nucleus is about 10⁻¹⁵ m across, while the whole atom is about 10⁻¹⁰ m: if the atom were a sports stadium, the nucleus would be a pea on the centre spot, yet it holds more than 99.9% of the mass.

Particle	Relative mass	Relative charge	Actual mass (kg)	Location
Proton, p	1	+1	1.673 × 10⁻²⁷	nucleus
Neutron, n	1	0	1.675 × 10⁻²⁷	nucleus
Electron, e⁻	1/1836	−1	9.109 × 10⁻³¹	around the nucleus

The number of protons, the atomic number Z, defines the element: every atom with 17 protons is chlorine. In a neutral atom the number of electrons equals Z. Electrons decide how an atom reacts; the nucleus decides its mass and whether it is radioactive.

Nuclide notation

A particular kind of nucleus is called a nuclide. It is written with the mass number A at the top left and the atomic number Z at the bottom left of the symbol. The number of neutrons is N = A − Z.

Nuclide notation for chlorine-37.

The same nuclide can be written in words as chlorine-37 or Cl-37. For an ion, the charge goes at the top right, and the number of electrons is Z minus the charge.

Counting particles in ions

State the number of protons, neutrons and electrons in $^{32}_{16}\text{S}^{2-}$ and in $^{56}_{26}\text{Fe}^{3+}$.

Sulfide ion: 16 protons; 32 − 16 = 16 neutrons; a charge of 2− means two extra electrons, so 16 + 2 = 18 electrons.

Iron(III) ion: 26 protons; 56 − 26 = 30 neutrons; a charge of 3+ means three electrons lost, so 26 − 3 = 23 electrons.

Isotopes

Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A). Carbon-12, carbon-13 and carbon-14 all have 6 protons and 6 electrons, but 6, 7 and 8 neutrons.

Isotopes have the same chemical properties, because chemistry depends on electrons and they have the same electron arrangement.
Isotopes have slightly different physical properties that depend on mass. Heavy water, D₂O (deuterium is hydrogen-2), has a density of 1.11 g mL⁻¹ and boils at 101.4 °C. Lighter molecules diffuse slightly faster, which is one way uranium-235 has been enriched for nuclear fuel.
Some isotopes are stable and some are radioactive. Carbon-12 and carbon-13 are stable; carbon-14 is not (lesson 1C).

Relative atomic mass

Atoms are far too light to weigh in kilograms conveniently, so chemists compare them with a standard. The relative atomic mass, Ar, of an element is the weighted mean mass of its atoms, relative to one twelfth of the mass of a carbon-12 atom, which is defined as exactly 12. It has no units. One twelfth of a carbon-12 atom is the atomic mass unit, 1 u = 1.661 × 10⁻²⁷ kg.

The relative isotopic masses and their abundances are measured with a mass spectrometer. It turns atoms into positive ions, accelerates them, separates them according to their mass-to-charge ratio (m/z) and counts how many arrive at each m/z. For singly charged ions, m/z is just the mass. Each isotope gives one peak, and the height of the peak shows its relative abundance.

$$A_r = \frac{\sum (\text{isotopic mass} \times \text{abundance})}{100}$$

Mass spectra of chlorine. Atoms give two peaks; Cl₂ molecules give three, because each molecule contains two atoms picked at random.

Ar from isotopic data

Magnesium consists of ²⁴Mg (78.99%, mass 23.985), ²⁵Mg (10.00%, mass 24.986) and ²⁶Mg (11.01%, mass 25.983). Calculate the relative atomic mass of magnesium.

$A_r = \dfrac{(23.985 \times 78.99) + (24.986 \times 10.00) + (25.983 \times 11.01)}{100}$

$= \dfrac{1894.6 + 249.9 + 286.1}{100} = 24.31$

Check: the answer is closest to 24, the most abundant isotope, as it should be.

Finding abundances from Ar

Copper has two isotopes, ⁶³Cu (mass 62.93) and ⁶⁵Cu (mass 64.93), and Ar = 63.55. Calculate the percentage abundance of each.

Let the fraction of ⁶³Cu be x, so the fraction of ⁶⁵Cu is 1 − x.

$62.93x + 64.93(1 - x) = 63.55 \Rightarrow 64.93 - 2.00x = 63.55 \Rightarrow x = 0.69$

So about 69% ⁶³Cu and 31% ⁶⁵Cu. (The accepted values are 69.15% and 30.85%.)

InteractiveIsotopes and relative atomic mass

Try this

Pick Cl and turn on Show working. Confirm that Ar = 35.45.
Switch to Molecules X₂⁺. You should see peaks at m/z 70, 72 and 74 with heights of about 100, 64 and 10. Why is there no peak for a Cl atom of mass 72?
Try Br as molecules. Explain why bromine gives three peaks in a 1 : 2 : 1 ratio.
Choose Pb. Which isotope does Ar = 207.22 sit closest to, and why?
Choose Ga ? and slide the abundance until Ar = 69.72. You should land on about 60.1% gallium-69. Check it with algebra.

Test yourself

How many neutrons are in one atom of $^{235}_{92}\text{U}$?
Which species has 18 electrons and 20 neutrons?
Boron is 19.9% ¹⁰B (mass 10.01) and 80.1% ¹¹B (mass 11.01). Its Ar is
Isotopes of the same element have the same
The mass spectrum of bromine vapour (Br₂) shows peaks at m/z 158, 160 and 162 in the ratio 1 : 2 : 1. This shows that

Label the parts of the nuclide symbol.

Compare carbon-12 and carbon-14 atoms.

The number of protons in a nucleus is the . Atoms of the same element with different numbers of neutrons are called . Relative atomic masses are measured relative to the isotope. The instrument used to measure isotopic abundance is a , which separates ions by their .

4 marks

Silver has two naturally occurring isotopes: ¹⁰⁷Ag (isotopic mass 106.91) and ¹⁰⁹Ag (isotopic mass 108.90). The relative atomic mass of silver is 107.87. Calculate the percentage abundance of each isotope and sketch the expected mass spectrum of silver atoms.

Your answer