Isotopes

1. Overview

Most elements occur naturally as a mixture of atoms that differ only in the number of neutrons in the nucleus. These atoms are isotopes. This section covers how to define isotopes, how to read the notation that shows an isotope's nucleon and proton numbers, and why isotopes of one element react in the same way yet differ in mass and density. These ideas lead straight into relative atomic mass (section 2.1).

Key Definitions

• Isotopes: atoms of the same element that have the same number of protons but different numbers of neutrons in the nucleus.
• Proton number (atomic number): the number of protons in the nucleus of an atom; every atom of an element has the same proton number, so it identifies the element.
• Nucleon number (mass number): the total number of protons and neutrons in the nucleus of an atom.
• Nucleon: a particle found in the nucleus of an atom, that is, a proton or a neutron.
• Neutron number: the number of neutrons in the nucleus of an atom, found by subtracting the proton number from the nucleon number.
• Isotope notation: a way of writing an isotope with its nucleon number at the top left of the element's symbol and its proton number at the bottom left, for example ³⁷₁₇Cl for chlorine-37; the charge of an ion goes at the top right.
• Chemical properties: the reactions a substance undergoes; they depend on the number and arrangement of electrons, so isotopes of one element have the same chemical properties.
• Physical properties of isotopes: properties that do not involve a reaction; for isotopes you need mass and density, which differ because the isotopes have different numbers of neutrons.
• Density: the mass of a substance per unit volume, density = mass ÷ volume, usually given in g cm⁻³ for solids and liquids and in g dm⁻³ for gases.

Content

What makes atoms isotopes

Every atom has a tiny nucleus, with electrons in shells around it (section 1.1). The nucleus contains protons and, in every atom except hydrogen-1, neutrons. The number of protons decides which element the atom is. Every atom with 17 protons is chlorine; every atom with 6 protons is carbon.

Atoms of one element can still have different numbers of neutrons. Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Chlorine has two stable isotopes:

	Chlorine-35	Chlorine-37
Protons	17	17
Neutrons	18	20
Electrons (neutral atom)	17	17
Nucleon number (protons + neutrons)	35	37

Two atoms are isotopes of each other only if both conditions hold:

1. Same number of protons, so they are the same element.
2. Different numbers of neutrons, so they have different nucleon numbers.

Matching nucleon numbers are not enough. Argon-40 (18 protons, 22 neutrons) and calcium-40 (20 protons, 20 neutrons) have the same nucleon number but different proton numbers, so they are different elements, not isotopes.

Most elements occur naturally as a mixture of isotopes. Some, such as fluorine and sodium, have only one stable isotope. Hydrogen's isotopes have their own names: deuterium (symbol D, or ²H) has one neutron, and tritium (³H) has two. Tritium is radioactive.

Isotope notation

The full notation puts two numbers to the left of the element's symbol:

$${}^{x}_{y}\text{A}$$

Here A is the symbol of the element, $x$ (top left) is the nucleon number (also called the mass number) and $y$ (bottom left) is the proton number (also called the atomic number). The number of neutrons is the difference between them:

$$\text{number of neutrons} = x - y$$

For ${}^{37}_{17}\text{Cl}$: 17 protons, and $37 - 17 = 20$ neutrons.

You will see the same isotope written in several ways: ${}^{37}_{17}\text{Cl}$, ${}^{37}\text{Cl}$, Cl-37 and chlorine-37. The proton number is often left out because the symbol already fixes it. If you need it, read it from the Periodic Table.

Ions. The charge goes at the top right, for example ${}^{37}_{17}\text{Cl}^{-}$. Forming an ion changes only the number of electrons. The protons and neutrons stay the same:

$$\text{number of electrons} = \text{proton number} - \text{charge}$$

So ${}^{37}_{17}\text{Cl}^{-}$ has $17 - (-1) = 18$ electrons, and ${}^{40}_{20}\text{Ca}^{2+}$ has $20 - 2 = 18$ electrons.

Do not mix this up with the Periodic Table. In the Periodic Table in the data booklet, the number above each symbol is the proton number. The number at the bottom of each box, under the name, such as 35.5 for chlorine, is the relative atomic mass. That value is an average over all the isotopes of the element (section 2.1), not a nucleon number, so never use it to count neutrons.

Worked example 1: reading isotope notation

Question: Four atoms are shown: A ${}^{58}_{28}\text{Ni}$, B ${}^{60}_{28}\text{Ni}$, C ${}^{59}_{27}\text{Co}$ and D ${}^{60}_{27}\text{Co}$.

(a) Give the numbers of protons, neutrons and electrons in each atom. (b) Which pairs are isotopes of the same element? (c) Which two atoms have the same number of neutrons? Explain why they are not isotopes. (d) Give the numbers of protons, neutrons and electrons in the ion ${}^{60}_{28}\text{Ni}^{2+}$.

Step 1: read each symbol. Protons = bottom number. Neutrons = top number − bottom number. In a neutral atom, electrons = protons.

Atom	Protons	Neutrons	Electrons
A ${}^{58}_{28}\text{Ni}$	28	58 − 28 = 30	28
B ${}^{60}_{28}\text{Ni}$	28	60 − 28 = 32	28
C ${}^{59}_{27}\text{Co}$	27	59 − 27 = 32	27
D ${}^{60}_{27}\text{Co}$	27	60 − 27 = 33	27

Step 2: find the isotopes. Look for the same bottom number with different top numbers. A and B both have 28 protons (nickel). C and D both have 27 protons (cobalt). B and D share the nucleon number 60, but they have different proton numbers, so they are different elements.

Step 3: compare neutrons. B and C both have 32 neutrons. B has 28 protons and C has 27, so they are atoms of different elements, and isotopes must be the same element.

Step 4: the ion. A 2+ charge means two electrons have been lost: $28 - 2 = 26$ electrons. The nucleus is unchanged.

Answer: (a) A: 28 protons, 30 neutrons, 28 electrons; B: 28, 32, 28; C: 27, 32, 27; D: 27, 33, 27. (b) A and B (nickel-58 and nickel-60); C and D (cobalt-59 and cobalt-60). (c) B and C; they have different numbers of protons, so they are different elements. (d) 28 protons, 32 neutrons, 26 electrons.

Why isotopes have the same chemical properties

Statement: isotopes of the same element have the same chemical properties. They take part in the same reactions, form the same products and are described by the same equations.

Explanation, as a chain of three links:

1. Isotopes have the same number of protons, so their neutral atoms have the same number of electrons.
2. The same nuclear charge holds the same number of electrons in the same way, so the isotopes have the same electronic configuration: the same arrangement of electrons in shells, sub-shells and orbitals.
3. Chemical reactions involve electrons only: outer electrons are lost, gained or shared. Neutrons have no charge, so they do not change the number or the arrangement of the electrons. So isotopes react in the same way.

For example, chlorine-35 and chlorine-37 atoms both have the configuration 1s² 2s² 2p⁶ 3s² 3p⁵. Both gain one electron to form a chloride ion, Cl⁻, and both react with sodium to form sodium chloride:

$$2\text{Na(s)} + \text{Cl}_2\text{(g)} \rightarrow 2\text{NaCl(s)}$$

The equation is the same whichever isotope the chlorine contains.

"Same number of protons" or "same number of outer electrons" is not a full explanation on its own. Sodium and potassium both have one outer electron, yet potassium reacts with water more vigorously. What gives isotopes the same chemical properties is the same number of electrons in the same arrangement.

You may meet data showing that a bond to a heavier isotope is very slightly stronger, for example a C-D bond compared with a C-H bond. This small difference comes from the mass of the atoms, not from the electrons, and it does not change which reactions happen, the products or the equations. It is beyond this course: in your answers, isotopes of an element have the same chemical properties.

Why isotopes have different physical properties: mass and density

Statement: isotopes of the same element have different physical properties. You need two: mass and density.

Mass. A neutron has almost the same mass as a proton, and an electron's mass is negligible in comparison. So each extra neutron adds about one unit of relative mass to an atom. An atom of chlorine-37 has a greater mass than an atom of chlorine-35 because it has two more neutrons. The mass of one mole of atoms of an isotope, in grams, is very close to its nucleon number: about 35 g for chlorine-35 and 37 g for chlorine-37.

The same number of extra neutrons matters far more in a light atom:

Isotopes compared	Extra neutrons in the heavier atom	Mass of heavier atom ÷ mass of lighter atom
hydrogen-1 and hydrogen-2 (deuterium)	1	2.00
lithium-6 and lithium-7	1	1.17
chlorine-35 and chlorine-37	2	1.06
uranium-235 and uranium-238	3	1.01

Of all the elements, hydrogen has the largest percentage difference in mass between its isotopes.

Density. Density is mass per unit volume. The size of an atom is set by its electrons, and isotopes have the same electrons. The nucleus is tiny compared with the whole atom (section 1.1), so extra neutrons do not change the atom's size noticeably. Compare two samples under the same conditions:

• the same number of particles takes up the same volume, but
• each particle of the heavier isotope has more mass, so
• there is more mass in each unit of volume: the density is greater.

Gases. At the same temperature and pressure, one mole of any gas occupies the same volume (24.0 dm³ at room conditions, treating the gas as ideal). Heavier atoms move more slowly on average, but at the same temperature they have the same average kinetic energy, so the same number of them in the same volume exerts the same pressure. A gas's density is therefore proportional to its molar mass.

Liquids and solids. The particles of two isotopic forms are almost the same size and pack in almost the same way, so the density is close to proportional to the mass of each particle. Worked example 3 tests this idea with "heavy water", D₂O, whose molecules contain deuterium atoms in place of ¹H atoms. Compounds made from different isotopes differ in the same way as the elements do.

Other physical properties, such as the boiling point of heavy water, also differ slightly, but you are only asked about mass and density.

Worked example 2: two flasks of argon

Question: Two sealed flasks each have a volume of 360 cm³. One holds pure argon-36 and the other pure argon-40, both at room conditions.

(a) Calculate the amount of gas, in mol, in each flask. (b) Calculate the mass and the density of the gas in each flask. (c) Calculate the mass of one atom of argon-40.

(Molar masses: argon-36, 36.0 g mol⁻¹; argon-40, 40.0 g mol⁻¹. $V_{\text{m}}$ = 24.0 dm³ mol⁻¹ at room conditions. $L$ = 6.022 × 10²³ mol⁻¹.)

Step 1: amount of gas. Convert the volume: 360 cm³ = 0.360 dm³. Both flasks are at the same temperature and pressure, so the amount does not depend on which isotope is present: $$n = \frac{V}{V_{\text{m}}} = \frac{0.360}{24.0} = 0.0150\ \text{mol}$$

Step 2: mass, from $m = nM$. $$\text{argon-36: } m = 0.0150 \times 36.0 = 0.540\ \text{g} \qquad \text{argon-40: } m = 0.0150 \times 40.0 = 0.600\ \text{g}$$

Step 3: density, from $\rho = m/V$. $$\text{argon-36: } \rho = \frac{0.540}{0.360} = 1.50\ \text{g dm}^{-3} \qquad \text{argon-40: } \rho = \frac{0.600}{0.360} = 1.67\ \text{g dm}^{-3}$$

Step 4: mass of one atom. One mole contains $L$ atoms, so $$m_{\text{atom}} = \frac{M}{L} = \frac{40.0}{6.022 \times 10^{23}} = 6.64 \times 10^{-23}\ \text{g}$$

Answer: (a) 0.0150 mol in each flask. (b) Argon-36: 0.540 g and 1.50 g dm⁻³. Argon-40: 0.600 g and 1.67 g dm⁻³. (c) $6.64 \times 10^{-23}$ g (3 s.f.).

Both flasks hold the same number of atoms in the same volume, so the ratio of the densities equals the ratio of the atomic masses: $40.0 \div 36.0 = 1.11$. If a question gives a temperature and pressure instead of naming room conditions, find $n$ with $pV = nRT$ (section 4.1).

Worked example 3: predicting the density of heavy water

Question: Heavy water, D₂O, contains deuterium atoms (D, ²H) in place of ordinary hydrogen atoms (¹H). Ordinary water, H₂O, has a density of 1.00 g cm⁻³ at room temperature. Predict the density of heavy water at the same temperature. Assume that D₂O molecules are the same size as H₂O molecules and pack in the same way. (Relative masses: ¹H = 1.0, D = 2.0, O = 16.0.)

Step 1: relative molecular masses. $$M_{\text{r}}(\text{H}_2\text{O}) = 2(1.0) + 16.0 = 18.0 \qquad M_{\text{r}}(\text{D}_2\text{O}) = 2(2.0) + 16.0 = 20.0$$

Step 2: use the assumption. The assumption is reasonable because the size of a molecule is set by its electrons, and D₂O and H₂O have the same electrons. Same size and same packing means the same number of molecules in each cm³. So the density is proportional to the mass of each molecule: $$\rho(\text{D}_2\text{O}) = \rho(\text{H}_2\text{O}) \times \frac{M_{\text{r}}(\text{D}_2\text{O})}{M_{\text{r}}(\text{H}_2\text{O})}$$

Step 3: substitute. $$\rho(\text{D}_2\text{O}) = 1.00 \times \frac{20.0}{18.0} = 1.11\ \text{g cm}^{-3}$$

Answer: about 1.11 g cm⁻³ (3 s.f.), 11% denser than ordinary water.

The measured density of heavy water at room temperature is about 1.10 g cm⁻³, slightly below this prediction but within 1% of it. So the extra mass of each molecule explains almost all of the difference. The small gap tests the assumption: a mole of D₂O takes up very slightly more volume than a mole of H₂O, so the assumption is very good but not exact. Heavy water is dense enough that ice made from it sinks in ordinary water.

Putting it together: a model explanation

Question: Lithium has two stable isotopes, lithium-6 and lithium-7. State and explain how their chemical properties and their physical properties compare.

A full answer covers four points:

1. Particles. Both atoms have 3 protons and 3 electrons. Lithium-6 has 3 neutrons and lithium-7 has 4.
2. Chemical properties: the same. Both have the same number of electrons and the same electronic configuration, 1s² 2s¹. Reactions involve electrons, not neutrons, so both isotopes react in the same way. For example, both react with water: $2\text{Li(s)} + 2\text{H}_2\text{O(l)} \rightarrow 2\text{LiOH(aq)} + \text{H}_2\text{(g)}$.
3. Mass: different. A lithium-7 atom has one more neutron, so it has a greater mass than a lithium-6 atom.
4. Density: different. The atoms are the same size and pack in the same way, so the same number of atoms fills each cm³. A sample of lithium-7 metal therefore has a greater density than a sample of lithium-6 metal.

Key Equations

Neutrons in a nucleus ($x$ = nucleon number, top left; $y$ = proton number, bottom left): $$\text{number of neutrons} = x - y$$

Electrons in an ion (charge with its sign: subtract 2 for a 2+ ion, add 1 for a 1− ion): $$\text{number of electrons} = \text{proton number} - \text{charge}$$

Density ($\rho$ in g cm⁻³ or g dm⁻³; $m$ = mass in g; $V$ = volume in cm³ or dm³): $$\rho = \frac{m}{V}$$

A gas at room conditions ($n$ = amount in mol; $V$ in dm³; $M$ = molar mass in g mol⁻¹; $\rho$ in g dm⁻³; $V_{\text{m}}$ = 24.0 dm³ mol⁻¹ at room conditions only, otherwise use $pV = nRT$): $$n = \frac{V}{V_{\text{m}}} \qquad \rho = \frac{M}{V_{\text{m}}}$$

Mass of one atom ($M$ in g mol⁻¹; $L$ = Avogadro constant, 6.022 × 10²³ mol⁻¹; answer in g): $$m_{\text{atom}} = \frac{M}{L}$$

Two isotopic forms of a substance with the same number of particles per unit volume (exact for ideal gases at the same temperature and pressure, approximate for liquids and solids): $$\frac{\rho_2}{\rho_1} = \frac{M_2}{M_1}$$

Common Mistakes to Avoid

• Mistake: treating the nucleon number as the number of neutrons. Fix: nucleon number = protons + neutrons. Cobalt-59 has a nucleon number of 59 but only $59 - 27 = 32$ neutrons.
• Mistake: a vague definition, such as "the same element with a different mass", or one that does not name both protons and neutrons, or leaves out the word "atoms". Fix: name both particles: "atoms of the same element with the same number of protons but different numbers of neutrons".
• Mistake: counting neutrons from the relative atomic mass in the Periodic Table. Fix: a number of neutrons is always a whole number; use the nucleon number of the isotope. For chlorine, $35.5 - 17 = 18.5$ is impossible; chlorine-37 has $37 - 17 = 20$ neutrons.
• Mistake: explaining why isotopes have the same chemical properties with only "same number of protons" or "same number of outer electrons", or saying the heavier isotope reacts differently. Fix: give the full chain: same number of electrons, same electronic configuration, and reactions involve electrons, not neutrons. Sodium and potassium both have one outer electron but do not react identically, while chlorine-35 and chlorine-37 both form Cl⁻ and NaCl by the same equation.
• Mistake: saying the heavier isotope is denser because its atoms are bigger or have more electrons. Fix: the atoms are the same size with the same electrons; only the mass differs. In Worked example 2, 0.0150 mol of each argon isotope fills the same 0.360 dm³, giving 1.50 g dm⁻³ for argon-36 and 1.67 g dm⁻³ for argon-40.
• Mistake: changing the protons or neutrons when an atom becomes an ion. Fix: only the electrons change. ${}^{60}_{28}\text{Ni}^{2+}$ has 28 protons, 32 neutrons and $28 - 2 = 26$ electrons.
• Mistake: writing "isotope" when you mean "isomer". Fix: isotopes are atoms of one element, such as chlorine-35 and chlorine-37. Isomers are different compounds with the same molecular formula, such as butane and methylpropane, both C₄H₁₀.

Exam Tips

• Define isotopes in one sentence that mentions atoms, protons and neutrons.
• Determine or complete a table of particles by working the same way every time: protons from the bottom number (or the Periodic Table), neutrons = top number − bottom number, electrons = protons − charge. Every answer must be a whole number.
• State and explain for chemical properties: first state "the same", then give the full chain of reasons: the same number of electrons, the same electronic configuration, and reactions involve electrons, not neutrons.
• State and explain for physical properties: name the property (mass or density), say which isotope has the greater value, and give the cause: more neutrons, so more mass. For density, add that the atoms are the same size, so the same volume holds more mass.
• Compare with both isotopes named and a direction: "an atom of chlorine-37 has a greater mass than an atom of chlorine-35", not "they have different masses".