Chapter 3 of 8

All 8 chapters
  1. 1Inside the atom, readunderstood
  2. 2How the model of the atom changed, readunderstood
  3. 3Isotopes, readunderstood
  4. 4Electron shells, readunderstood
  5. 5The periodic table, readunderstood
  6. 6Ionic bonding, readunderstood
  7. 7Covalent bonding, readunderstood
  8. 8Metals and alloys, readunderstood

S4.6.3 Chapter 3

Isotopes

Atoms have a whole number of particles. So why is the mass of chlorine in the periodic table 35.5?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Explain what isotopes are and why they react the same way
  • Calculate relative atomic mass from isotope amounts

The number of protons decides which element an atom is. But the number of neutrons can change. Atoms of one element are not all the same.

Isotopes are atoms of the same element with the same number of protons and different numbers of neutrons. They have the same atomic number and different mass numbers.

Draw it first

Two isotopes of chlorine

  1. Two chlorine atoms side by side. The first, labelled chlorine 35, has a nucleus with 17p and 18n, that is 17 protons and 18 neutrons, and electrons on three shells. The second, labelled chlorine 37, has 17p and 20n. A line under both says same protons and electrons.17p18nchlorine 35

    1 Chlorine 35 has 17 protons, 18 neutrons and 17 electrons. Its mass number is 35.

  2. Two chlorine atoms side by side. The first, labelled chlorine 35, has a nucleus with 17p and 18n, that is 17 protons and 18 neutrons, and electrons on three shells. The second, labelled chlorine 37, has 17p and 20n. A line under both says same protons and electrons.17p18nchlorine 3517p20nchlorine 37

    2 Chlorine 37 has 17 protons, 20 neutrons and 17 electrons. Its mass number is 37.

  3. Two chlorine atoms side by side. The first, labelled chlorine 35, has a nucleus with 17p and 18n, that is 17 protons and 18 neutrons, and electrons on three shells. The second, labelled chlorine 37, has 17p and 20n. A line under both says same protons and electrons.17p18nchlorine 3517p20nchlorine 37same protons and electrons

    3 The two atoms have the same protons and the same electrons. Only the neutrons differ.

We write the element and its mass number in words: chlorine 35 and chlorine 37. Chemists also write the numbers beside the symbol, as you saw in Chapter 1.

Two chlorine atoms in nuclide notation. On the left the symbol Cl has 35 at the top and 17 at the bottom. On the right the symbol Cl has 37 at the top and 17 at the bottom.3517Cl3717Cl
The top numbers differ. The bottom numbers are the same.

Hydrogen has three well known isotopes. Most hydrogen atoms have no neutron at all.

A table of three hydrogen isotopes with the columns Isotope and Neutrons. Hydrogen 1 has 0 neutrons. Hydrogen 2 has 1 neutron. Hydrogen 3 has 2 neutrons. Every hydrogen atom has 1 proton.IsotopeNeutronshydrogen 10hydrogen 21hydrogen 32
Every hydrogen atom has 1 proton and 1 electron. Hydrogen 3 is unstable, so it is radioactive.

Why do isotopes react in the same way? A chemical reaction is about electrons, above all the outer ones. Isotopes of an element have the same number of electrons. So they react the same way.

The extra neutrons add mass. They do not change the electrons, so isotopes take part in the same reactions. Isotopes do differ in a few things that depend on mass, such as density. A few isotopes are also unstable. That is a topic of its own.

Now look again at the periodic table box. The number at the bottom of the box is the relative atomic mass. It is the mean mass of the atoms of an element, on a scale where a carbon 12 atom is exactly 12.

It is a mean because a sample of an element holds a mixture of isotopes. The mean depends on how much of each isotope there is. This amount is its abundance, often written as a percentage of all the atoms.

A bar chart of the abundance of chlorine isotopes. The axis is labelled percentage of atoms, with a scale from 0 to 100 in steps of 25. The bar for chlorine 35 reaches 75. The bar for chlorine 37 reaches 25.0255075100chlorine 35chlorine 37percentage of atoms
Out of every 100 chlorine atoms, about 75 are chlorine 35 and 25 are chlorine 37.

Take 100 chlorine atoms. Find their total mass, then divide by 100. Chlorine 35 is more common, so it pulls the mean closer to 35 than to 37. Counting this way is called a weighted mean.

Worked example

Chlorine is 75% chlorine 35 and 25% chlorine 37. Find its relative atomic mass.

  1. Think of 100 atoms: 75 have mass number 35 and 25 have mass number 37.
  2. Total mass = 75 × 35 + 25 × 37 = 2 625 + 925 = 3 550.
  3. Mean mass = 3 550 ÷ 100 = 35.5.

Answer: 35.5

No single chlorine atom has a mass of 35.5. It is the mean, like a class where the mean number of children in a family is 2.4.

Worked example

Magnesium is 79% magnesium 24, 10% magnesium 25 and 11% magnesium 26. Find its relative atomic mass to one decimal place.

  1. In 100 atoms, 79 have mass number 24, 10 have 25 and 11 have 26.
  2. Total mass = 79 × 24 + 10 × 25 + 11 × 26 = 1 896 + 250 + 286 = 2 432.
  3. Mean mass = 2 432 ÷ 100 = 24.32, which is 24.3 to one decimal place.

Answer: 24.3

Try it

Find a mean with paper pieces

You need: a sheet of paper, torn into 20 small pieces, a pencil, a cup or bowl.

  1. On 15 pieces write the number 35. On the other 5 pieces write 37.
  2. Mix the pieces in the cup. Each piece stands for one chlorine atom.
  3. Add up all the numbers on the 20 pieces.
  4. Divide the total by 20.
  5. Look through the pieces. Is there one with your answer written on it?

What you will see: The total is 710. Divide by 20 and you get 35.5. Not one piece has 35.5 on it. The mean is a number for the whole mixture, not for any one atom.

If you cannot try it, this is what happens.
A table of the paper pieces with the columns Number and Pieces. The number 35 is on 15 pieces. The number 37 is on 5 pieces.NumberPieces3515375

A wrong idea many people have

Isotopes of an element react in different ways, because they have different masses.

Why it feels right: Atoms with a different mass number look like different atoms, so it seems they should behave differently.

The test that breaks it: Look at what a reaction needs. Chlorine 35 and chlorine 37 both have 17 electrons, with 7 in the outer shell. Both gain one electron to react with sodium, in the same way.

What is true: Isotopes of one element react the same way, because they have the same electrons. Only properties that depend on mass, such as density, differ, and some isotopes are radioactive.

Key words

isotopes
atoms of one element with the same number of protons and different numbers of neutrons.
relative atomic mass
the mean mass of the atoms of an element, on a scale where a carbon 12 atom is exactly 12.
abundance
how much of an isotope there is, often as a percentage of all the atoms.

Back to your guess

The answer is B: Chlorine atoms differ in mass, and 35.5 is the mean of them.

Chlorine is a mixture of two kinds of atom with different masses. The relative atomic mass, 35.5, is the mean of all of them.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Carbon has atoms with 6, 7 and 8 neutrons. What is the same in all of these atoms?

    Tap your answer.

    1. Not this one. The neutrons are what differ. That is why the atoms are different isotopes. Try another.

    2. Not this one. The mass number is protons plus neutrons. With different neutrons, the mass number differs. Try another.

    3. Yes, that is right. All carbon atoms have the same number of protons, and that is what makes them carbon. The neutrons can differ.

    See the answer

    The number of protons

    All carbon atoms have the same number of protons, and that is what makes them carbon. The neutrons can differ.

    • If you chose A: The neutrons are what differ. That is why the atoms are different isotopes.
    • If you chose B: The mass number is protons plus neutrons. With different neutrons, the mass number differs.

  2. Why do isotopes of an element react in the same way?

    Tap your answer.

    1. Not this one. Isotopes differ in mass, because they have different numbers of neutrons. Reactions depend on electrons. Try another.

    2. Not this one. Isotopes have different numbers of neutrons. The same electrons make the reactions the same. Try another.

    3. Not this one. They are different in mass, but they are still the same element. The sameness of the electrons is the reason. Try another.

    4. Yes, that is right. Reactions are about electrons. Isotopes have the same protons, so the same number of electrons, and so the same reactions.

    See the answer

    They have the same number of electrons.

    Reactions are about electrons. Isotopes have the same protons, so the same number of electrons, and so the same reactions.

    • If you chose A: Isotopes differ in mass, because they have different numbers of neutrons. Reactions depend on electrons.
    • If you chose B: Isotopes have different numbers of neutrons. The same electrons make the reactions the same.
    • If you chose C: They are different in mass, but they are still the same element. The sameness of the electrons is the reason.

  3. A neon atom has 10 protons and mass number 22. How many neutrons does it have?

    Tap your answer.

    1. Yes, that is right. Neutrons = mass number − atomic number = 22 − 10 = 12. Neon 20 has 10 neutrons, so this isotope has 2 more.

    2. Not this one. That is the mass number. It counts the protons too, so take the protons away. Go to S4.6.1. Try another.

    3. Not this one. That is the number of protons. Neutrons = mass number − atomic number. Go to S4.6.1. Try another.

    See the answer

    12 neutrons

    Neutrons = mass number − atomic number = 22 − 10 = 12. Neon 20 has 10 neutrons, so this isotope has 2 more.

    • If you chose B: That is the mass number. It counts the protons too, so take the protons away. Go to S4.6.1.
    • If you chose C: That is the number of protons. Neutrons = mass number − atomic number. Go to S4.6.1.

  4. The relative atomic mass of chlorine is 35.5. What does this tell us?

    Tap your answer.

    1. Not this one. No atom has half a particle. The 35.5 is a mean over a mixture of atoms. Try another.

    2. Yes, that is right. Chlorine atoms have mass numbers of 35 and 37. The mean, weighted by how many there are of each, is 35.5.

    3. Not this one. Neutrons are whole particles. The half comes from averaging atoms of mass 35 and 37. Try another.

    See the answer

    It is the mean mass of chlorine atoms, which are a mixture of isotopes.

    Chlorine atoms have mass numbers of 35 and 37. The mean, weighted by how many there are of each, is 35.5.

    • If you chose A: No atom has half a particle. The 35.5 is a mean over a mixture of atoms.
    • If you chose C: Neutrons are whole particles. The half comes from averaging atoms of mass 35 and 37.

  5. Boron is 20% boron 10 and 80% boron 11. What is its relative atomic mass?

    A bar chart of boron isotopes. The axis is labelled percentage of atoms, with a scale from 0 to 100 in steps of 25. The bar for boron 10 reaches 20. The bar for boron 11 reaches 80.0255075100boron 10boron 11percentage of atoms
    Tap your answer.

    1. Not this one. You found the plain mean of 10 and 11. Boron 11 is far more common, so it counts for more. Go to M4.7.2. Try another.

    2. Not this one. Boron 11 is the most common, but there is some boron 10, so the mean is a little lower. Try another.

    3. Yes, that is right. (20 × 10 + 80 × 11) ÷ 100 = (200 + 880) ÷ 100 = 1 080 ÷ 100 = 10.8.

    See the answer

    10.8

    (20 × 10 + 80 × 11) ÷ 100 = (200 + 880) ÷ 100 = 1 080 ÷ 100 = 10.8.

    • If you chose A: You found the plain mean of 10 and 11. Boron 11 is far more common, so it counts for more. Go to M4.7.2.
    • If you chose B: Boron 11 is the most common, but there is some boron 10, so the mean is a little lower.

  6. How do you work out a relative atomic mass from the isotopes?

    Tap your answer.

    1. Yes, that is right. Each isotope counts as much as its share of the atoms. That is a weighted mean.

    2. Not this one. That is a plain mean. It ignores how common each isotope is. Go to M4.7.2. Try another.

    3. Not this one. That is close, but not exact. Every isotope counts in proportion to its share. Try another.

    See the answer

    Multiply each mass number by its percentage, add, and divide by the total of the percentages.

    Each isotope counts as much as its share of the atoms. That is a weighted mean.

    • If you chose B: That is a plain mean. It ignores how common each isotope is. Go to M4.7.2.
    • If you chose C: That is close, but not exact. Every isotope counts in proportion to its share.

  7. From an earlier chapter

    Which model of the atom first put electrons on fixed shells?

    Tap your answer.

    1. Not this one. Rutherford showed a nucleus, but he did not put the electrons on shells. Go to S4.6.2. Try another.

    2. Yes, that is right. Niels Bohr placed each electron on a shell at a set distance from the nucleus.

    3. Not this one. Thomson spread his electrons through a positive ball. There were no shells. Go to S4.6.2. Try another.

    See the answer

    The shell model of Bohr

    Niels Bohr placed each electron on a shell at a set distance from the nucleus.

    • If you chose A: Rutherford showed a nucleus, but he did not put the electrons on shells. Go to S4.6.2.
    • If you chose C: Thomson spread his electrons through a positive ball. There were no shells. Go to S4.6.2.

  8. An atom of potassium 41 has atomic number 19. How many neutrons does it have?

    See the answer

    22 neutrons

    41 − 19 = 22.

  9. Element X has two isotopes. 75% of its atoms have mass number 20 and 25% have mass number 22. What is its relative atomic mass?

    See the answer

    20.5

    (75 × 20 + 25 × 22) ÷ 100 = (1 500 + 550) ÷ 100 = 2 050 ÷ 100 = 20.5.

Keep it

Copy this into your exercise book.

Isotopes: same protons, different neutrons, so the same reactions. Relative atomic mass is a weighted mean: add mass × percentage for each isotope, then divide by 100. Chlorine: 35.5.

Draw: Two chlorine atoms with 17p and 18n, and 17p and 20n, and the sum that gives 35.5.

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