Answer key · Unit 1

Atoms and elements.

Each lesson’s practice questions, their correct answers and the mistakes they spot. Answers read off the Scene use the same setting the learner sees.

Misconception catalogue

Answer key 7

Lesson 1 of 7 · About 20 minutes

Inside an atom

Three particles build every atom: protons and neutrons in a tiny nucleus, electrons around it. The atomic number decides the element, and the mass number counts everything in the nucleus.

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The 5 steps and their answers

Step 1 of 5
Open this step
Three particles
Practice · Choose
Question
A carbon atom has six protons, six neutrons and six electrons. Where is almost all of its mass?

Correct answer
- Correct In the nucleus
Setup, choices and feedback
The Scene at this step
Protons
6
Electron view
Shells
Choices
Shown in a random order.
- Correct In the nucleus
- Wrong In the electrons, since they take up most of the atom’s volume
  Misconception: Thinks the electrons carry a good share of the atom’s mass, because they fill its volume.
  Feedback from the catalogue
  The electrons fill almost all of the atom’s volume, but carry almost none of its mass: each electron is $1836$ ⁠ times lighter than a proton. More than $99.9\%$ ⁠ of an atom’s mass is in the tiny nucleus, in its protons and neutrons.
- Wrong Half in the nucleus, half in the electrons
  Misconception: Thinks the electrons carry a good share of the atom’s mass, because they fill its volume.
  Feedback from the catalogue
  The electrons fill almost all of the atom’s volume, but carry almost none of its mass: each electron is $1836$ ⁠ times lighter than a proton. More than $99.9\%$ ⁠ of an atom’s mass is in the tiny nucleus, in its protons and neutrons.
Feedback for a right answer
In the nucleus. Six protons and six neutrons make $12$ ⁠ mass units, and the six electrons together weigh about $0.003$ ⁠ of a unit. The electrons take up nearly all of the atom’s volume, but almost none of its mass.

Hint
Compare the mass of an electron with that of a proton.

Worked solution
1. Relative mass: proton $1$ ⁠, neutron $1$ ⁠, electron $\tfrac{1}{1836}$ ⁠.
2. In the nucleus: $6 + 6 = 12$ ⁠.
3. The electrons: $6 \times \tfrac{1}{1836} \approx 0.003$ ⁠.
4. So more than $99.9\%$ ⁠ of the mass is in the nucleus.
If you chose the electrons, you mixed up volume and mass: the electrons decide how much room the atom takes up, not how much it weighs.
Step 2 of 5
Open this step
The atomic number
Practice · Choose
Question
The Scene shows an oxygen atom. Which of these decides that it is oxygen and not another element?

Correct answer
- Correct The number of protons in the nucleus
Setup, choices and feedback
The Scene at this step
Protons
8
Electron view
Shells
Choices
Shown in a random order.
- Correct The number of protons in the nucleus
- Wrong The number of neutrons in the nucleus
  Misconception: Thinks the number of neutrons, or the mass, decides which element an atom is.
  Feedback from the catalogue
  The element is decided only by the number of protons, the atomic number $Z$ ⁠. Atoms of one element can differ in their number of neutrons, and so in mass: those are the isotopes. Carbon-12 and carbon-13 are both carbon; to make nitrogen you need a seventh proton.
- Wrong The atom’s mass
  Misconception: Thinks the number of neutrons, or the mass, decides which element an atom is.
  Feedback from the catalogue
  The element is decided only by the number of protons, the atomic number $Z$ ⁠. Atoms of one element can differ in their number of neutrons, and so in mass: those are the isotopes. Carbon-12 and carbon-13 are both carbon; to make nitrogen you need a seventh proton.
- Wrong The number of electrons around the nucleus
  Feedback
  An atom can gain or lose electrons and stay the same element: an oxygen ion, with ten electrons, is still oxygen. Only the number of protons defines the element.
Feedback for a right answer
The atomic number, $Z = 8$ ⁠, is the number of protons, and it alone makes this oxygen. An oxygen atom with nine or ten neutrons is still oxygen, and an atom with nine protons is already fluorine.

Hint
What do all the oxygen atoms in the world have in common?

Worked solution
1. An element is defined by its atomic number, $Z$ ⁠.
2. $Z$ ⁠ is the number of protons in the nucleus.
3. Every atom with $Z = 8$ ⁠ is oxygen, whatever its numbers of neutrons or electrons.
If you chose the mass or the neutrons: oxygen has three kinds of stable atom, with $8$ ⁠, $9$ ⁠ and $10$ ⁠ neutrons and different masses, and all of them are oxygen.
Step 3 of 5
Open this step
The mass number
Practice · Calculate
Question
The aluminium atom in the Scene has $Z = 13$ ⁠, and its mass number is $A = 27$ ⁠. How many neutrons are in its nucleus?

Correct answer
14 ± 0.01
Setup, choices and feedback
The Scene at this step
Protons
13fixed
Electron view
Shells
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Neutrons in the most common isotope/nodes/atom/outputs/neutrons
Wrong answers it recognises
- 27 ± 0.01
  Misconception: Takes the mass number as the number of neutrons or of electrons.
  Feedback from the catalogue
  The mass number $A$ ⁠ counts every particle in the nucleus: protons and neutrons together. To find the number of neutrons, subtract the atomic number from it, $N = A - Z$ ⁠. The number of electrons in a neutral atom equals the number of protons, $Z$ ⁠.
- 13 ± 0.01
  Misconception: Assumes every atom has as many neutrons as protons.
  Feedback from the catalogue
  Only some light atoms, such as carbon-12 and oxygen-16, have as many neutrons as protons. The heavier the atom, the more neutrons it has beyond its protons: aluminium has $14$ ⁠ neutrons and $13$ ⁠ protons, lead $126$ ⁠ neutrons and $82$ ⁠ protons. Always work out $N = A - Z$ ⁠.
Feedback for a right answer
$N = A - Z = 27 - 13 = 14$ ⁠. Light atoms have about as many neutrons as protons, and in heavier atoms the neutrons start to pull ahead.

Hint
The mass number counts the protons too.

Worked solution
1. The givens: $Z = 13$ ⁠, $A = 27$ ⁠.
2. $A = Z + N$ ⁠, so $N = A - Z$ ⁠.
3. $N = 27 - 13 = 14$ ⁠ neutrons.
If you answered $27$ ⁠, you gave the mass number, which counts every particle in the nucleus. If you answered $13$ ⁠, you assumed one neutron for every proton; that holds only for some light atoms.
Step 4 of 5
Open this step
Writing an atom
Practice · Calculate
Question
A neutral potassium atom is $^{39}_{19}\mathrm{K}$ ⁠. How many electrons does it have?

Correct answer
19 ± 0.01
Setup, choices and feedback
The Scene at this step
Protons
19fixed
Electron view
Shells
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Electrons in the neutral atom, equal to Z/nodes/atom/outputs/electrons
Wrong answers it recognises
- 39 ± 0.01
  Misconception: Takes the mass number as the number of neutrons or of electrons.
  Feedback from the catalogue
  The mass number $A$ ⁠ counts every particle in the nucleus: protons and neutrons together. To find the number of neutrons, subtract the atomic number from it, $N = A - Z$ ⁠. The number of electrons in a neutral atom equals the number of protons, $Z$ ⁠.
- 20 ± 0.01
  Misconception: Takes the mass number as the number of neutrons or of electrons.
  Feedback
  $20$ ⁠ is the number of neutrons, $39 - 19$ ⁠. But electrons balance the charge of the protons, and neutrons have no charge.
Feedback for a right answer
$19$ ⁠: the lower number is the atomic number, the number of protons, and a neutral atom has one electron for every proton. You can count them in the Scene: 2,8,8,1.

Hint
In a neutral atom the charges cancel.

Worked solution
1. In the symbol $^{39}_{19}\mathrm{K}$ ⁠ the lower number is $Z = 19$ ⁠, and the upper one $A = 39$ ⁠.
2. $Z$ ⁠ is the number of protons: $19$ ⁠.
3. The atom is neutral, so it has as many electrons as protons: $19$ ⁠.
If you answered $39$ ⁠, you counted the mass number; it counts protons and neutrons, not electrons.
Step 5 of 5
Open this step
Finding an atom by its mass
Practice · Reach the target
Question
Change Protons until the atom in the Scene has a mass number of $24$ ⁠, then press Check.

Goal
- 24 ± 0.1
  At the start of the step: 12
Setup, choices and feedback
The Scene at this step
Protons
6
Electron view
Shells
Read from the Scene at
Mass number A = Z + N of the most common isotope/nodes/atom/outputs/massNumber
One setting that reaches it
Protons
12
Feedback for a right answer
Magnesium, $^{24}_{12}\mathrm{Mg}$ ⁠: 12 protons and 12 neutrons. The mass number alone is not enough to identify an element, but here only one element has a common atom of this mass.

Feedback for a wrong answer
Not yet. Start from $Z = 12$ ⁠, half of $24$ ⁠, and check the mass number.

Hint
For light elements the mass number is about twice the atomic number.

Worked solution
1. For light elements $N \approx Z$ ⁠, so $A \approx 2Z$ ⁠.
2. $2Z = 24$ ⁠ gives $Z = 12$ ⁠.
3. Set Protons to $12$ ⁠: magnesium, $12$ ⁠ protons and $12$ ⁠ neutrons, $A = 24$ ⁠.
Sodium, $Z = 11$ ⁠, gives $A = 23$ ⁠, and aluminium, $Z = 13$ ⁠, already $A = 27$ ⁠.

Lesson 2 of 7 · About 25 minutes

Isotopes

Atoms of the same element with different numbers of neutrons: what they are called, why their chemistry is the same, and how the mixture found in nature sets the relative atomic mass in the periodic table.

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The 5 steps and their answers

Step 1 of 5
Open this step
One more neutron
Practice · Predict, then look
Question
The nucleus in the Scene has six protons and six neutrons: carbon-12. What do you get by adding one neutron?

Correct answer
- Correct Carbon-13: the same element, heavier
Setup, choices and feedback
The Scene at this step
Protons
6
Neutrons
6
Nucleus / Every nucleus
Nucleus
Choices
- Correct Carbon-13: the same element, heavier
- Wrong Nitrogen: the next element in the table
  Misconception: Thinks the number of neutrons, or the mass, decides which element an atom is.
  Feedback from the catalogue
  The element is decided only by the number of protons, the atomic number $Z$ ⁠. Atoms of one element can differ in their number of neutrons, and so in mass: those are the isotopes. Carbon-12 and carbon-13 are both carbon; to make nitrogen you need a seventh proton.
- Wrong A carbon ion, with an electric charge
  Feedback
  A neutron has no charge, so adding one does not change the nucleus’s charge. An ion forms when an atom gains or loses electrons.
Once the prediction is locked in, the Scene changes
Neutrons
7
The Scene then shows: 13 · Mass number A = Z + N/nodes/nucleus/outputs/massNumber
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Carbon-13, $^{13}_{6}\mathrm{C}$ ⁠: still six protons, so still carbon, and the mass number has gone up to $13$ ⁠. It is stable, and one carbon atom in a hundred in nature is carbon-13.

Worked solution
1. The element is set by the number of protons, $Z = 6$ ⁠, which has not changed.
2. The mass number: $A = Z + N = 6 + 7 = 13$ ⁠.
3. You get carbon-13, an isotope of carbon.
If you predicted nitrogen: nitrogen needs a seventh proton, not a neutron.
Step 2 of 5
Open this step
Naming an isotope
Practice · Reach the target
Question
Chlorine is $Z = 17$ ⁠. Use Protons and Neutrons to build the nucleus of chlorine-37, then press Check.

Goal
- 17 ± 0.1
  At the start of the step: 6
- 37 ± 0.1
  At the start of the step: 12
Setup, choices and feedback
The Scene at this step
Protons
6
Neutrons
6
Nucleus / Every nucleus
Nucleus
Read from the Scene at
Protons/nodes/nucleus/props/protons
Read from the Scene at
Mass number A = Z + N/nodes/nucleus/outputs/massNumber
One setting that reaches it
Protons
17
Neutrons
20
Feedback for a right answer
$17$ ⁠ protons and $20$ ⁠ neutrons: $^{37}_{17}\mathrm{Cl}$ ⁠. Chlorine-35, the common isotope, has $18$ ⁠ neutrons.

Feedback for a wrong answer
Not yet. Set $17$ ⁠ protons, and work out how many neutrons make up $37$ ⁠.

Hint
The name chlorine-37 gives the mass number, not the number of neutrons.

Worked solution
1. Chlorine: $Z = 17$ ⁠, so set Protons to $17$ ⁠.
2. Chlorine-37: $A = 37$ ⁠.
3. $N = A - Z = 37 - 17 = 20$ ⁠, so set Neutrons to $20$ ⁠.
If you set $37$ ⁠ neutrons, you made $A = 54$ ⁠: the name counts every particle in the nucleus.
Step 3 of 5
Open this step
The same chemistry
Practice · Choose
Question
Carbon-12 and carbon-14 build exactly the same molecules: carbon dioxide, sugar, proteins. Why?

Correct answer
- Correct Both have six electrons, arranged the same way
Setup, choices and feedback
The Scene at this step
Protons
6
Neutrons
8
Nucleus / Every nucleus
Light nuclei
Choices
Shown in a random order.
- Correct Both have six electrons, arranged the same way
- Wrong Both have the same mass
  Feedback
  Their masses differ: carbon-14 is heavier than carbon-12 by two neutrons, about $17\%$ ⁠.
- Wrong They do not really react the same way: carbon-14 is radioactive, so its chemistry is different
  Misconception: Thinks isotopes of one element react differently, for instance because one is radioactive.
  Feedback from the catalogue
  An atom’s chemistry is decided by its electrons, and every isotope of an element has the same number of electrons, arranged the same way. So they build the same molecules. What differs is the nucleus: the mass, and whether it is stable. Radioactivity belongs to the nucleus, not to the bonds.
Feedback for a right answer
Chemistry is decided by the electrons, and both isotopes have six electrons arranged 2,4. The nucleus affects the mass and the stability, not the bonds.

Hint
Which part of the atom do other atoms touch when they bond?

Worked solution
1. Both isotopes have $Z = 6$ ⁠: six protons.
2. A neutral atom also has six electrons, arranged the same way, 2,4.
3. Chemical bonds form between the outer electrons, so the chemistry is the same.
Carbon-14’s radioactivity belongs to the nucleus: it decides when the atom will turn into nitrogen, not what it bonds to until then.
Step 4 of 5
Open this step
The natural mixture
Practice · Calculate
Question
Out of every hundred chlorine atoms in nature, $75.8$ ⁠ are chlorine-35 and $24.2$ ⁠ are chlorine-37. What is chlorine’s relative atomic mass? Give two decimal places.

Correct answer
35.45 ± 0.05
Setup, choices and feedback
The Scene at this step
Protons
17fixed
Neutrons
18
Nucleus / Every nucleus
Nucleus
Accepted within
± 0.05
Computed from the Scene at this step’s setting
The element's relative atomic mass: its isotopes' masses (u) weighted by abundance/nodes/nucleus/outputs/relativeAtomicMass
Wrong answers it recognises
- 36 ± 0.05
  Misconception: Averages the isotope masses without weighting them by how common each one is.
  Feedback from the catalogue
  Relative atomic mass is a weighted mean: each isotope counts by how common it is in nature. For chlorine, where three atoms in four are chlorine-35, the mean is $35.45$ ⁠, not $36$ ⁠, halfway between $35$ ⁠ and $37$ ⁠. A plain mean is right only when the isotopes are equally common.
Feedback for a right answer
$A_r \approx 35.5$ ⁠. The mean is close to $35$ ⁠, because three atoms in four are chlorine-35. The periodic table gives $35.45$ ⁠: the exact calculation uses the isotopes’ exact masses, which are not quite whole numbers.

Hint
Multiply each mass number by how common it is, add, and divide by $100$ ⁠.

Worked solution
1. The givens: $75.8\%$ ⁠ of mass $35$ ⁠, and $24.2\%$ ⁠ of mass $37$ ⁠.
2. A weighted mean: $A_r = \dfrac{75.8 \times 35 + 24.2 \times 37}{100}$ ⁠.
3. $75.8 \times 35 = 2653$ ⁠, and $24.2 \times 37 = 895.4$ ⁠.
4. $A_r = \dfrac{3548.4}{100} \approx 35.48$ ⁠, about $35.5$ ⁠.
If you answered $36$ ⁠, you took a plain mean of $35$ ⁠ and $37$ ⁠, as if the two isotopes were equally common.
Step 5 of 5
Open this step
Reading the mean
Practice · Choose
Question
Copper’s relative atomic mass is $63.55$ ⁠, and it has two stable isotopes: copper-63 and copper-65. Which is more common in nature?

Correct answer
- Correct Copper-63
Setup, choices and feedback
The Scene at this step
Protons
17
Neutrons
18
Nucleus / Every nucleus
Nucleus
Choices
Shown in a random order.
- Correct Copper-63
- Wrong Copper-65
  Feedback
  If most atoms were copper-65, the mean would be close to $65$ ⁠. But $63.55$ ⁠ is closer to $63$ ⁠.
- Wrong Both are equally common
  Misconception: Averages the isotope masses without weighting them by how common each one is.
  Feedback from the catalogue
  Relative atomic mass is a weighted mean: each isotope counts by how common it is in nature. For chlorine, where three atoms in four are chlorine-35, the mean is $35.45$ ⁠, not $36$ ⁠, halfway between $35$ ⁠ and $37$ ⁠. A plain mean is right only when the isotopes are equally common.
Feedback for a right answer
Copper-63: the mean, $63.55$ ⁠, is pulled towards the common isotope. In fact about $69\%$ ⁠ of copper atoms are copper-63.

Hint
Which of the two numbers is the mean closer to?

Worked solution
1. A weighted mean lies closer to the more common value.
2. If the two were equally common, $A_r$ ⁠ would be $\dfrac{63 + 65}{2} = 64$ ⁠.
3. $63.55 < 64$ ⁠, so copper-63 is the more common.
4. A check: if $x$ ⁠ is the share of copper-63, $63x + 65(1 - x) = 63.55$ ⁠ gives $x \approx 0.72$ ⁠, close to the measured $69\%$ ⁠.

Lesson 3 of 7 · About 25 minutes

Electron shells

How electrons settle into shells, how to write the arrangement, why the outer shell decides the chemistry, and how the shells build the rows and columns of the periodic table.

Open the lesson

The 5 steps and their answers

Step 1 of 5
Open this step
Filling the shells
Practice · Choose
Question
What is the electron arrangement of magnesium, $Z = 12$ ⁠?

Correct answer
- Correct 2,8,2
Setup, choices and feedback
The Scene at this step
Protons
10
Electron view
Shells
Choices
Shown in a random order.
- Correct 2,8,2
- Wrong 2,10
  Misconception: Lets a shell hold any number of electrons, such as ten in the second shell or eight in the first.
  Feedback from the catalogue
  Each shell has a capacity: the first has room for only two electrons, the second for eight. For the elements up to calcium the third also takes eight before the fourth begins. Once a shell is full, the next electron starts a new shell, further from the nucleus: so sodium is 2,8,1, not 2,9.
- Wrong 8,4
  Misconception: Lets a shell hold any number of electrons, such as ten in the second shell or eight in the first.
  Feedback from the catalogue
  Each shell has a capacity: the first has room for only two electrons, the second for eight. For the elements up to calcium the third also takes eight before the fourth begins. Once a shell is full, the next electron starts a new shell, further from the nucleus: so sodium is 2,8,1, not 2,9.
- Wrong 2,2,8
  Feedback
  Electrons fill the inner shells first. A new shell starts only once the one before it is full.
Feedback for a right answer
2,8,2: two electrons fill the first shell, eight the second, and two start the third. Set Protons to $12$ ⁠ and count.

Hint
Two in the first, eight in the second, and the rest in the third.

Worked solution
1. Magnesium has $12$ ⁠ electrons.
2. The first shell holds $2$ ⁠: $10$ ⁠ left.
3. The second holds $8$ ⁠: $2$ ⁠ left.
4. The last two go into the third shell: 2,8,2.
2,10 puts more than eight in the second shell, and 8,4 puts more than two in the first.
Step 2 of 5
Open this step
The outer electrons
Practice · Calculate
Question
The Scene shows phosphorus, $Z = 15$ ⁠. How many electrons are in its outer shell?

Correct answer
5 ± 0.01
Setup, choices and feedback
The Scene at this step
Protons
15fixed
Electron view
Shells
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Electrons in the outermost occupied shell/nodes/atom/outputs/outerElectrons
Wrong answers it recognises
- 15 ± 0.01
  Misconception: Counts all of an atom’s electrons, or its shells, as its outer electrons.
  Feedback from the catalogue
  The outer electrons are only those in the last, outermost shell. To find them, write the full arrangement filling from the inside: $2$ ⁠, then $8$ ⁠, and the rest in the last shell. Phosphorus, 2,8,5, has five outer electrons, not $15$ ⁠, and three shells.
- 3 ± 0.01
  Misconception: Counts all of an atom’s electrons, or its shells, as its outer electrons.
  Feedback
  $3$ ⁠ is phosphorus’s number of shells, not the number of electrons in the last one.
Feedback for a right answer
$5$ ⁠: the arrangement is 2,8,5. Like nitrogen, above it in the table, phosphorus has five outer electrons, and both are in group 15.

Hint
Write the electron arrangement first.

Worked solution
1. Phosphorus has $15$ ⁠ electrons.
2. $2$ ⁠ in the first shell and $8$ ⁠ in the second: $15 - 10 = 5$ ⁠ left.
3. Those five are in the third, outer shell: 2,8,5.
If you answered $15$ ⁠, you counted every electron. Only those in the last shell touch other atoms.
Step 3 of 5
Open this step
A full shell
Practice · Predict, then look
Question
Neon in the Scene is 2,8: two full shells. Add one proton, and with it an electron. Where does the new electron go?

Correct answer
- Correct Into a new, third shell
Setup, choices and feedback
The Scene at this step
Protons
10
Electron view
Shells
Choices
- Correct Into a new, third shell
- Wrong Into the second shell, which now holds nine
  Misconception: Lets a shell hold any number of electrons, such as ten in the second shell or eight in the first.
  Feedback from the catalogue
  Each shell has a capacity: the first has room for only two electrons, the second for eight. For the elements up to calcium the third also takes eight before the fourth begins. Once a shell is full, the next electron starts a new shell, further from the nucleus: so sodium is 2,8,1, not 2,9.
- Wrong Into the first shell, nearest the nucleus
  Feedback
  The first shell is already full with two electrons, from helium on.
Once the prediction is locked in, the Scene changes
Protons
11
The Scene then shows: 3 · Shells holding at least one electron/nodes/atom/outputs/shells
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Sodium, 2,8,1: the eleventh electron starts a third shell, far from the nucleus. That is why sodium gives it up so easily, and reacts so violently.

Worked solution
1. Neon: 2,8, both shells full.
2. The second shell holds at most $8$ ⁠.
3. Electron number $11$ ⁠ has to start a third shell: 2,8,1, sodium.
Step 4 of 5
Open this step
Rows and columns
Practice · Reach the target
Question
The Scene shows fluorine: second row, seven outer electrons, group 17. Change Protons until you reach the element below it in the table, in the third row and the same group, then press Check.

Goal
- 3 ± 0.1
  At the start of the step: 2
- 17 ± 0.1
  At the start of the step: 17
Setup, choices and feedback
The Scene at this step
Protons
9
Electron view
Shells
Read from the Scene at
Row of the periodic table: the number of occupied shells/nodes/atom/outputs/period
Read from the Scene at
Column of the periodic table, 1, 2 or 13–18 (helium 18)/nodes/atom/outputs/group
One setting that reaches it
Protons
17
Feedback for a right answer
Chlorine, $Z = 17$ ⁠, 2,8,7: three shells and seven outer electrons. In the table it sits right below fluorine, and like fluorine it is a halogen.

Feedback for a wrong answer
Not yet. You need three shells, with seven electrons in the third.

Hint
Third row means three shells; group 17 means seven electrons in the outer one.

Worked solution
1. Third row: the first two shells are full, $2 + 8 = 10$ ⁠ electrons.
2. Group 17: seven electrons in the third shell.
3. That makes $10 + 7 = 17$ ⁠ electrons, so $17$ ⁠ protons: chlorine.
Step 5 of 5
Open this step
Families
Practice · Choose
Question
Which of these elements is most like sodium, $Z = 11$ ⁠, in its chemistry?

Correct answer
- Correct Potassium, $Z = 19$ ⁠
Setup, choices and feedback
The Scene at this step
Protons
3
Electron view
Shells
Choices
Shown in a random order.
- Correct Potassium, $Z = 19$ ⁠
- Wrong Magnesium, $Z = 12$ ⁠
  Misconception: Thinks elements next to each other in a row behave alike, rather than those in the same column.
  Feedback from the catalogue
  Neighbours in a row are very different: sodium is a violently reactive metal, and neon beside it is a noble gas that hardly reacts at all. Likeness goes by the column: elements in one group have the same number of outer electrons, so their chemistry is alike.
- Wrong Neon, $Z = 10$ ⁠
  Misconception: Thinks elements next to each other in a row behave alike, rather than those in the same column.
  Feedback from the catalogue
  Neighbours in a row are very different: sodium is a violently reactive metal, and neon beside it is a noble gas that hardly reacts at all. Likeness goes by the column: elements in one group have the same number of outer electrons, so their chemistry is alike.
- Wrong Chlorine, $Z = 17$ ⁠
  Misconception: Thinks elements next to each other in a row behave alike, rather than those in the same column.
  Feedback from the catalogue
  Neighbours in a row are very different: sodium is a violently reactive metal, and neon beside it is a noble gas that hardly reacts at all. Likeness goes by the column: elements in one group have the same number of outer electrons, so their chemistry is alike.
Feedback for a right answer
Potassium, 2,8,8,1: like sodium, 2,8,1, it has a single outer electron. Both are soft alkali metals that react violently with water, potassium even more violently.

Hint
Write each one’s electron arrangement and compare the outer shells.

Worked solution
1. Sodium: 2,8,1, one outer electron.
2. Potassium: 2,8,8,1, one outer electron.
3. Magnesium: 2,8,2; neon: 2,8; chlorine: 2,8,7.
4. Only potassium has the same outer shell, so it is in the same group and like sodium.
Magnesium and neon are close to sodium in atomic number, but chemistry goes by the column, not by the neighbours in a row.

Lesson 4 of 7 · About 25 minutes

Trends in the periodic table

Reading the periodic table: row and group, metals and non-metals, and the two key trends, atom size and ionisation energy, along a row and down a group, and why they run in opposite directions.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
Reading the table
Practice · Reach the target
Question
Change Atomic number until the latest element in the table is the one in the fourth row and group 2, then press Check.

Goal
- 4 ± 0.1
  At the start of the step: 3
- 2 ± 0.1
  At the start of the step: 1
Setup, choices and feedback
The Scene at this step
Atomic number
11
Column height
Flat tiles
Rearrange the table
Families
Read from the Scene at
Row of the latest element, 1–7/nodes/table/outputs/period
Read from the Scene at
Column of the latest element, 1–18; 0 in the f-block/nodes/table/outputs/group
One setting that reaches it
Atomic number
20
Column height
Flat tiles
Feedback for a right answer
Calcium, $Z = 20$ ⁠: the second element of the fourth row, with two outer electrons, below magnesium.

Feedback for a wrong answer
Not yet. Fill the table to the start of the fourth row, and go one step further.

Hint
The fourth row starts with potassium, $Z = 19$ ⁠.

Worked solution
1. The third row ends at argon, $Z = 18$ ⁠.
2. The fourth row starts with potassium, $Z = 19$ ⁠, in group 1.
3. The next element, $Z = 20$ ⁠, is in group 2: calcium.
Step 2 of 6
Open this step
Metals and non-metals
Practice · Choose
Question
Which of these third-row elements is a metal?

Correct answer
- Correct Magnesium
Setup, choices and feedback
The Scene at this step
Atomic number
118
Column height
Flat tiles
Rearrange the table
Families
Choices
Shown in a random order.
- Correct Magnesium
- Wrong Silicon
  Feedback
  Silicon is shiny like a metal, but it is brittle and conducts electricity only a little: a metalloid, on the staircase.
- Wrong Sulfur
  Feedback
  Sulfur is a brittle yellow non-metal, on the right of the table.
- Wrong Chlorine
  Feedback
  Chlorine is a greenish gas, a halogen: a clear non-metal.
Feedback for a right answer
Magnesium, in group 2: a light, shiny metal that burns with a dazzling white light. Moving right along a row, the elements become less and less metallic.

Hint
The metals are on the left of the table.

Worked solution
1. Place each element in the third row: magnesium in group 2, silicon in 14, sulfur in 16, chlorine in 17.
2. The metals are on the left, up to the staircase.
3. Only magnesium is left of the staircase: it is the metal.
Step 3 of 6
Open this step
Atom size along a row
Practice · Predict, then look
Question
From sodium to argon, each element adds a proton to the nucleus and an electron to the outer shell. What happens to atom size along the third row?

Correct answer
- Correct It shrinks
Setup, choices and feedback
The Scene at this step
Atomic number
11
Column height
Atom sizefixed
Rearrange the table
Families
Choices
- Correct It shrinks
- Wrong It grows, because there are more electrons
  Misconception: Thinks atoms grow along a row because they gain electrons.
  Feedback from the catalogue
  Along a row the extra electrons go into the same outer shell, not a new one. Meanwhile the nucleus gains a proton at every step and pulls that shell harder inwards. So atoms shrink along a row. They grow only down a group, where each row adds a whole shell.
- Wrong It hardly changes, because the number of shells is the same
  Feedback
  The number of shells is indeed the same, but the nucleus grows stronger at each step and pulls the same shell inwards.
Once the prediction is locked in, the Scene changes
Atomic number
18
The Scene then shows: 106 pm · Covalent radius of the latest element; NaN if not measured/nodes/table/outputs/radius
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
It shrinks, from 166 pm for sodium to about 100 pm for chlorine and argon. The nucleus adds positive charge at every step and pulls harder on the outer shell, which stays the same shell.

Worked solution
1. Along the row the number of shells is fixed: three.
2. At each step the nuclear charge goes up by $1$ ⁠.
3. A stronger nucleus pulls the same shell closer, so the atom shrinks.
If you predicted it grows: more electrons take up no more room when they go into the same shell.
Step 4 of 6
Open this step
Atom size down a group
Practice · Predict, then look
Question
Lithium’s radius is 128 pm, and sodium’s, one row below, 166 pm. Predict the size of a potassium atom, one row below sodium.

Correct answer
203 pm ± 25 pm
A number prediction counts as right within ± 25 pm
Setup, choices and feedback
The Scene at this step
Atomic number
11
Column height
Atom sizefixed
Rearrange the table
Families
Once the prediction is locked in, the Scene changes
Atomic number
19
The Scene then shows: 203 pm · Covalent radius of the latest element; NaN if not measured/nodes/table/outputs/radius
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
203 pm: each row adds a shell, and the atom grows by about another 40 pm. Potassium is the biggest of the elements so far, the peak of the columns of atom size.

Worked solution
1. From lithium to sodium the atom grows by 166 − 128 = 38 pm.
2. From sodium to potassium another whole shell is added, so expect a similar growth.
3. An estimate: 166 + 38 ≈ 204 pm. The measured value: 203 pm.
Step 5 of 6
Open this step
Pulling an electron off
Practice · Choose
Question
From which atom is it easiest to pull one electron off?

Correct answer
- Correct Sodium
Setup, choices and feedback
The Scene at this step
Atomic number
18
Column height
Ionisation energyfixed
Rearrange the table
Families
Choices
Shown in a random order.
- Correct Sodium
- Wrong Magnesium
  Feedback
  Magnesium is close, but its nucleus is one proton stronger than sodium’s, and holds its two outer electrons harder.
- Wrong Chlorine
  Misconception: Thinks an atom with more electrons gives one up more easily.
  Feedback from the catalogue
  What decides how hard an electron is to pull off is how hard the nucleus pulls on it: how close it is, and how many inner shells shield it. Along a row the nucleus grows stronger and the atom smaller, so ionisation energy rises: argon, with $18$ ⁠ electrons, needs three times as much as sodium.
- Wrong Argon, because it has the most electrons
  Misconception: Thinks an atom with more electrons gives one up more easily.
  Feedback from the catalogue
  What decides how hard an electron is to pull off is how hard the nucleus pulls on it: how close it is, and how many inner shells shield it. Along a row the nucleus grows stronger and the atom smaller, so ionisation energy rises: argon, with $18$ ⁠ electrons, needs three times as much as sodium.
Feedback for a right answer
Sodium: 496 kJ/mol, against 1521 kJ/mol for argon. Sodium’s single electron in the third shell is far from the nucleus and shielded by ten inner electrons.

Hint
Look for the lowest valley in the third row.

Worked solution
1. Along the row the nuclear charge grows, and the atom shrinks.
2. The closer the outer electron is to a stronger nucleus, the harder it is to pull off.
3. So the lowest ionisation energy in the row is at its start: sodium, 496 kJ/mol.
If you chose argon or chlorine: more electrons does not mean a looser electron. Argon has a full, small shell, and sits on a peak.
Step 6 of 6
Open this step
The peaks
Practice · Reach the target
Question
Change Atomic number until the latest element in the table is the third-row element with the highest ionisation energy, then press Check.

Goal
- 1521000 ± 1000
  At the start of the step: 496000
- 3 ± 0.1
  At the start of the step: 3
Setup, choices and feedback
The Scene at this step
Atomic number
11
Column height
Ionisation energyfixed
Rearrange the table
Families
Read from the Scene at
First ionisation energy of the latest element; NaN if not measured/nodes/table/outputs/ionisationEnergy
Read from the Scene at
Row of the latest element, 1–7/nodes/table/outputs/period
One setting that reaches it
Atomic number
18
Feedback for a right answer
Argon, $Z = 18$ ⁠: 1521 kJ/mol. A full outer shell, a small atom, and a nucleus of $18$ ⁠ protons: the peak of the row.

Feedback for a wrong answer
Not yet. Stay in the third row, and look for the tallest column.

Hint
Ionisation energy rises along the row up to the noble gas.

Worked solution
1. The third row: sodium to argon, $Z = 11$ ⁠ to $18$ ⁠.
2. Ionisation energy rises along the row, with small dips, up to the noble gas.
3. Set Atomic number to $18$ ⁠: argon.

Lesson 5 of 7 · About 25 minutes

Metalloids

The elements on the table's staircase: silicon shines like a metal yet shatters like glass, and conducts better the warmer it gets. What the band gap explains, and why arsenic and antimony behave like metals.

Open the lesson

The 5 steps and their answers

Step 1 of 5
Open this step
Shiny but brittle
Practice · Predict, then look
Question
Silicon has the grey shine of a metal. What happens when a lump of silicon is struck with a hammer?

Correct answer
- Correct It shatters, like glass
Setup, choices and feedback
The Scene at this step
Element
Siliconfixed
Temperature
300 K
Zoom to the bonds
Barfixed
Choices
- Correct It shatters, like glass
- Wrong It flattens out, like a lump of aluminium
  Misconception: Takes a shiny element to be a metal that bends, so expects silicon to flatten under a hammer.
  Feedback from the catalogue
  Shine alone does not make an element a metal. Silicon shines because it absorbs every visible colour in a thin skin and reflects a good share of it, but it has no sea of electrons: every outer electron is held in a bond in a fixed direction. A blow tears the bonds, and the crystal shatters.
- Wrong It keeps a small dent, like lead
  Misconception: Takes a shiny element to be a metal that bends, so expects silicon to flatten under a hammer.
  Feedback from the catalogue
  Shine alone does not make an element a metal. Silicon shines because it absorbs every visible colour in a thin skin and reflects a good share of it, but it has no sea of electrons: every outer electron is held in a bond in a fixed direction. A blow tears the bonds, and the crystal shatters.
Once the prediction is locked in, the Scene changes
Zoom to the bonds
Bondsfixed
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
It shatters. Each silicon atom shares a pair of electrons with each of four neighbours, and the bonds point in fixed directions. To move a row of atoms sideways the bonds have to break, so the crystal cracks instead of bending.

Worked solution
1. A metal has a sea of electrons, and its bond does not depend on any particular neighbour: rows of atoms slide over each other and the metal bends.
2. In silicon every outer electron is held in a bond between two particular atoms, in a fixed direction.
3. A blow moves rows of atoms, the bonds tear, and the crystal shatters.
The shine is no sign of a metal: silicon absorbs every visible colour in a thin skin, and a material that absorbs light that strongly also reflects a good share of it.
Step 2 of 5
Open this step
Warming silicon
Practice · Predict, then look
Question
Heat the silicon bar from Room, 300 K, to Hot plate, 600 K. What happens to its conductivity?

Correct answer
- Correct It rises enormously, thousands of times or more
Setup, choices and feedback
The Scene at this step
Element
Siliconfixed
Temperature
300 K
Zoom to the bonds
Bar
Choices
- Correct It rises enormously, thousands of times or more
- Wrong It falls a little, like a metal’s
  Misconception: Thinks heating always makes a material conduct worse, as it does a metal.
  Feedback from the catalogue
  In a metal the number of free electrons is fixed, and heat only shakes the atoms into their path, so it conducts a little worse. In a semiconductor such as silicon, heat frees electrons from their bonds, and their number climbs steeply: the conductivity rises hundreds and thousands of times.
- Wrong It stays the same: the bar has a fixed number of electrons
  Feedback
  The total number of electrons is fixed, but most are held in bonds and carry no current. Heat frees some of them, and only the freed ones conduct.
Once the prediction is locked in, the Scene changes
Temperature
600 K
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The needle climbs from about 0.0003 to about 15 S/m, tens of thousands of times. Heat shakes electrons out of their bonds, and the number freed climbs steeply with temperature.

Worked solution
1. In silicon almost all the outer electrons are held in bonds, and the band gap is 1.1 eV.
2. The hotter the bar, the more electrons get enough energy from heat to jump the gap.
3. Every freed electron, and every hole it leaves, carries current: the conductivity rises tens of thousands of times.
In a metal it is the other way round: the number of free electrons is fixed, and heat only shakes the atoms into their path.
Step 3 of 5
Open this step
One siemens per metre
Practice · Reach the target
Question
Change Temperature until the silicon bar conducts about 1 S/m, then press Check.

Goal
- 1 S/m ± 10%
  At the start of the step: 0.0003044 S/m
Setup, choices and feedback
The Scene at this step
Element
Siliconfixed
Temperature
300 K
Zoom to the bonds
Bar
Read from the Scene at
The bar's conductivity at this temperature/nodes/probe/outputs/conductivity
One setting that reaches it
Temperature
476 K
Feedback for a right answer
About 480 K, around 200 °C. Heating by just 180 degrees raised the conductivity about three thousand times.

Feedback for a wrong answer
Not yet. If the reading is below 1 S/m, heat more; if above, cool.

Hint
The reading under the chart shows the conductivity. Look between 450 and 500 K.

Worked solution
1. At 300 K the conductivity is about 0.0003 S/m, and at 600 K about 15 S/m: the target lies between.
2. At 400 K it is about 0.07 S/m, still low.
3. At 500 K it is about 1.8 S/m, a little too high.
4. About 480 K gives 1.0 S/m.
Step 4 of 5
Open this step
Two that behave like metals
Practice · Predict, then look
Question
Heat the arsenic bar from Room to Hot plate. What happens to its conductivity?

Correct answer
- Correct It falls, to about half
Setup, choices and feedback
The Scene at this step
Element
Arsenicfixed
Temperature
300 K
Zoom to the bonds
Bar
Choices
- Correct It falls, to about half
- Wrong It rises enormously, like silicon’s
  Misconception: Expects every metalloid to conduct better when heated, as silicon does.
  Feedback from the catalogue
  Not every metalloid is a semiconductor. Arsenic and antimony have no band gap: their bands overlap slightly, so they always have a fixed number of free electrons. Heat frees no more, it only scatters them, and the conductivity falls, as in a metal. They are semimetals.
- Wrong It does not change at all
  Feedback
  Arsenic’s number of free electrons is indeed fixed, but heat shakes the atoms, and they get in the electrons’ way.
Once the prediction is locked in, the Scene changes
Temperature
600 K
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The conductivity falls from about 3 × 10⁶ to about 1.4 × 10⁶ S/m, as a metal’s does. Arsenic has no gap for heat to help across: its number of free electrons is fixed, and heat only scatters them.

Worked solution
1. In arsenic the bands overlap slightly: there is no band gap, and a small, fixed number of electrons is always free.
2. Heat cannot free any more.
3. Heat does shake the atoms harder, and they get in the free electrons’ way: the conductivity falls, as in a metal.
Not every metalloid is a semiconductor: arsenic and antimony are semimetals.
Step 5 of 5
Open this step
Down group 14
Practice · Choose
Question
Germanium and silicon have exactly the same network, four bonds per atom. Why does germanium conduct thousands of times better at room temperature?

Correct answer
- Correct Its band gap is smaller, so heat frees far more electrons
Setup, choices and feedback
The Scene at this step
Element
Germanium
Temperature
300 K
Zoom to the bonds
Bonds
Choices
Shown in a random order.
- Correct Its band gap is smaller, so heat frees far more electrons
- Wrong It has a sea of free electrons, like a metal
  Feedback
  Then it would conduct worse when heated, like aluminium. But in the Scene germanium’s conductivity climbs with heat, like silicon’s.
- Wrong Each germanium atom makes more bonds
  Feedback
  In both crystals each atom is bonded to exactly four neighbours. The difference is how tightly the bond holds its electrons.
Feedback for a right answer
Germanium’s band gap, 0.7 eV, is smaller than silicon’s, 1.1 eV. Germanium atoms are bigger, and the bond electrons are farther from the nucleus, so they are easier to free.

Hint
Compare the band gap under the chart for the two elements.

Worked solution
1. The band gaps: diamond 5.5 eV, silicon 1.1 eV, germanium 0.7 eV.
2. Down group 14 the atoms get bigger, and the outer electrons are held less tightly.
3. The smaller the gap, the more electrons heat frees, and the better the bar conducts: in the Scene 1.9 S/m for germanium against 0.0003 S/m for silicon.

Lesson 6 of 7 · About 20 minutes

Non-metals

A cabinet of sixteen non-metals: why most are gases at room temperature, what stays whole when they melt and boil, how boiling points climb down the halogens, and why carbon is the exception.

Open the lesson

The 5 steps and their answers

Step 1 of 5
Open this step
Mostly gases
Practice · Calculate
Question
At room temperature, how many of the sixteen ampoules hold a gas?

Correct answer
10 ± 0.01
Setup, choices and feedback
The Scene at this step
Temperature
293 K
Show the molecules
Samples
Accepted within
± 0.01
Computed from the Scene at this step’s setting
How many of the 16 samples are gases at this temperature/nodes/cabinet/outputs/gases
Feedback for a right answer
Ten: hydrogen, nitrogen, oxygen, fluorine, chlorine, and the five noble gases from helium to xenon. Bromine is a liquid, and five are solids: carbon, phosphorus, sulfur, selenium and iodine.

Hint
An ampoule of gas looks empty or evenly tinted all through: it has no lump and no pool.

Worked solution
1. The noble gases: helium, neon, argon, krypton and xenon, five.
2. The small pairs: hydrogen, nitrogen, oxygen, fluorine and chlorine, five more.
3. $5 + 5 = 10$ ⁠.
Bromine, Br₂, is a dark red pool: a liquid, not a gas, though its vapour tints the ampoule.
Step 2 of 5
Open this step
Strong inside, weak between
Practice · Predict, then look
Question
Heat the cabinet to Red heat, 1000 K. What happens to molecules such as N₂, Cl₂ and S₈?

Correct answer
- Correct They stay whole, only moving apart and faster
Setup, choices and feedback
The Scene at this step
Temperature
293 K
Show the molecules
Molecules
Choices
- Correct They stay whole, only moving apart and faster
- Wrong They split into single atoms
  Misconception: Thinks melting or boiling a non-metal splits its molecules into atoms.
  Feedback from the catalogue
  Melting and boiling break only the weak pull between molecules. The strong bonds inside each molecule stay: nitrogen gas is still N₂, and boiling sulfur is still mostly S₈ rings. That is why so little heat is needed to boil non-metals.
- Wrong They join into one big network
  Feedback
  Heat separates molecules, it does not stick them together. Only the weak pull between them gives way.
Once the prediction is locked in, the Scene changes
Temperature
1000 K
The Scene then shows: 15 · How many of the 16 samples are gases at this temperature/nodes/cabinet/outputs/gases
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Fifteen of the samples are gases now, and every molecule is whole: pairs are still pairs, and sulfur’s rings are still rings. Melting and boiling broke only the weak pull between the molecules.

Worked solution
1. Every molecule has strong bonds between the atoms inside it.
2. Between separate molecules there is only a weak pull.
3. Boiling overcomes only the weak pull: the molecules move apart but stay whole.
Chlorine gas is still Cl₂, not single chlorine atoms.
Step 3 of 5
Open this step
Down the halogens
Practice · Predict, then look
Question
At room temperature fluorine and chlorine are gases and bromine is a liquid. What will iodine, I₂, below them in the column, be?

Correct answer
- Correct A solid
Setup, choices and feedback
The Scene at this step
Temperature
75 Kfixed
Show the molecules
Samples
Choices
- Correct A solid
- Wrong A liquid, like bromine
  Feedback
  The trend carries on: gas, gas, liquid, then solid. Iodine has more electrons than bromine, so the pull between its molecules is stronger still.
- Wrong A gas, like fluorine and chlorine
  Misconception: Expects bigger, heavier molecules to escape into a gas more easily, so to boil lower.
  Feedback from the catalogue
  The opposite: the weak pull between molecules grows with their number of electrons. Big, heavy molecules cling together more, and boil higher. Down the halogens: fluorine and chlorine are gases, bromine is a liquid, and iodine is a solid.
Once the prediction is locked in, the Scene changes
Temperature
293 Kfixed
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Iodine is a shiny grey-violet lump, and its faint violet vapour tints the ampoule a little. It melts only at 387 K.

Worked solution
1. Down the halogens the molecules get bigger: F₂, Cl₂, Br₂, I₂.
2. The more electrons a molecule has, the stronger the weak pull between it and its neighbours.
3. So melting and boiling points climb down the column: gas, gas, liquid, solid.
Step 4 of 5
Open this step
Liquid air
Practice · Predict, then look
Question
Cool the cabinet to 75 K, Liquid air. How many of the sixteen ampoules will still hold a gas?

Correct answer
3 ± 0.01
A number prediction counts as right within ± 0.01
Setup, choices and feedback
The Scene at this step
Temperature
293 Kfixed
Show the molecules
Samples
Once the prediction is locked in, the Scene changes
Temperature
75 Kfixed
The Scene then shows: 3 · How many of the 16 samples are gases at this temperature/nodes/cabinet/outputs/gases
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Three: hydrogen, which boils at 20 K, helium at 4 K and neon at 27 K. Nitrogen, oxygen, fluorine and argon are already liquid or close to it, and the rest are frozen.

Worked solution
1. Only an element whose boiling point is below 75 K stays a gas.
2. Helium 4 K, hydrogen 20 K, neon 27 K: three.
3. Nitrogen boils at 77 K, just above, so it is already liquid.
These are the smallest molecules and atoms, with the fewest electrons.
Step 5 of 5
Open this step
Carbon, the exception
Practice · Choose
Question
At 1000 K almost every non-metal is a gas, but carbon stays solid up to about 3900 K. Why?

Correct answer
- Correct Graphite has no small molecules: to vaporise it, the strong bonds themselves must break
Setup, choices and feedback
The Scene at this step
Temperature
1000 K
Show the molecules
Molecules
Choices
Shown in a random order.
- Correct Graphite has no small molecules: to vaporise it, the strong bonds themselves must break
- Wrong Carbon atoms are especially heavy
  Feedback
  A carbon atom, $12$ ⁠, is lighter than sulfur, chlorine or iodine atoms, which are all gases here. What matters is how the atoms are bonded, not what they weigh.
- Wrong Carbon is really a metal
  Feedback
  Carbon is a non-metal: it shares electrons in bonds. Graphite conducts along its sheets, but that is not what keeps it solid.
Feedback for a right answer
Each graphite sheet is one giant molecule, every atom in it bonded to three neighbours. There is no weak pull between small molecules to overcome, so it takes enormous heat.

Worked solution
1. In the other non-metals, melting and boiling break only a weak pull between small molecules.
2. In graphite every atom of a sheet is held by strong bonds: there are no small molecules to separate.
3. Turning carbon into vapour means breaking strong bonds, which happens only at about 3900 K.

Lesson 7 of 7 · About 30 minutes

Transition metals

The ten columns in the middle of the table: d electrons, ions of more than one charge, and why copper solutions are blue while zinc's are colourless. Ligand-field splitting, the colour left when white light loses one colour, and what ammonia changes.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
d electrons
Practice · Calculate
Question
An iron atom has $26$ ⁠ electrons: $18$ ⁠ like argon, two in 4s and six in 3d. How many d electrons does the Fe²⁺ ion have?

Correct answer
6 ± 0.01
Setup, choices and feedback
The Scene at this step
Metal ion
Fe²⁺fixed
Ammonia ligands
0 of 6
Zoom to the d orbitals
Test tubes
Accepted within
± 0.01
Computed from the Scene at this step’s setting
3d electrons of the chosen ion/nodes/rack/outputs/electrons
Wrong answers it recognises
- 4 ± 0.01
  Misconception: Removes a transition metal’s d electrons first when it forms an ion, rather than its outer 4s electrons.
  Feedback from the catalogue
  When a transition-metal atom becomes an ion, it gives up its outer-shell electrons, 4s, first, and only then d electrons. Iron has six 3d electrons and two in 4s, so Fe²⁺ keeps six d electrons, and Fe³⁺ five.
Feedback for a right answer
Six. The two electrons that leave are the 4s pair, and the six in 3d stay. The tube is labelled: 6 d electrons.

Hint
Which electrons leave first when the ion forms?

Worked solution
1. Iron: $18$ ⁠ like argon, plus $2$ ⁠ in 4s and $6$ ⁠ in 3d.
2. Fe²⁺ has given up two electrons, and both come from 4s.
3. $6$ ⁠ remain in 3d.
If you answered $4$ ⁠, you took both electrons out of 3d. But in the transition metals 4s empties first.
Step 2 of 6
Open this step
Several charges
Practice · Choose
Question
Why does iron form both Fe²⁺ and Fe³⁺, while sodium forms only Na⁺?

Correct answer
- Correct Iron’s 4s and 3d electrons have similar energies, so a third electron costs only a little more
Setup, choices and feedback
The Scene at this step
Metal ion
Cr³⁺
Ammonia ligands
0 of 6
Zoom to the d orbitals
Test tubes
Choices
Shown in a random order.
- Correct Iron’s 4s and 3d electrons have similar energies, so a third electron costs only a little more
- Wrong Iron has many more electrons in its outer shell
  Feedback
  Iron’s outer shell, 4s, holds only two. The third electron comes from 3d, whose energy is close.
- Wrong Fe³⁺ forms when Fe²⁺ gains another electron
  Feedback
  Gaining an electron, which is negative, would lower the charge. Fe³⁺ forms when iron gives up a third electron.
Feedback for a right answer
For sodium, a second electron would have to come from a full inner shell, at nine times the cost. For iron, a third electron, from 3d, costs only about twice as much, so both ions are common.

Worked solution
1. Sodium, 2,8,1: after the first electron a full shell is left, and opening it is very costly.
2. Iron gives up its two 4s electrons and becomes Fe²⁺.
3. The 3d electrons are close in energy, so giving up one more, to Fe³⁺, costs only about twice as much.
4. Both charges are within reach, so iron turns up in both.
Step 3 of 6
Open this step
Taking out a colour
Practice · Choose
Question
Ti³⁺ absorbs blue-green light and looks purple. Another solution absorbs mostly yellow light. What colour does it look?

Correct answer
- Correct Violet-blue
Setup, choices and feedback
The Scene at this step
Metal ion
Ti³⁺
Ammonia ligands
0 of 6
Zoom to the d orbitals
Test tubes
Choices
Shown in a random order.
- Correct Violet-blue
- Wrong Yellow
  Misconception: Thinks a solution looks the colour it absorbs.
  Feedback from the catalogue
  The eye sees the light that passed through the solution, not the light absorbed. A solution that absorbs yellow looks violet-blue, and Ti³⁺, which absorbs blue-green, looks purple: red and violet are left.
- Wrong Colourless
  Feedback
  A colourless solution absorbs no visible colour. Here one colour is taken out, and the rest reach the eye.
Feedback for a right answer
Take yellow out of white light and mostly blue and violet are left. The eye sees what passed through, not what was absorbed.

Worked solution
1. White light is every colour together.
2. The solution absorbs the yellow photons, whose energy equals Δ.
3. The colours that pass, mostly blue and violet, are what you see.
Ti³⁺ works the same way: it absorbs blue-green, leaving red and violet, which together look purple.
Step 4 of 6
Open this step
Colourless ions
Practice · Choose
Question
Solutions of which ions are colourless? Choose all that apply.

Correct answer
- Correct Sc³⁺
- Correct Zn²⁺
Setup, choices and feedback
The Scene at this step
Metal ion
Cu²⁺
Ammonia ligands
0 of 6
Zoom to the d orbitals
d orbitals
Choices
Shown in a random order. More than one choice is correct: every one must be selected.
- Correct Sc³⁺
- Correct Zn²⁺
- Wrong Cu²⁺
  Feedback
  Cu²⁺ has nine d electrons and one free place on the upper level: an electron can jump, and the solution is blue.
- Wrong Fe²⁺
  Feedback
  Fe²⁺’s band lies mostly in the infrared, but it reaches into the red, so the solution is a pale green, not colourless.
Feedback for a right answer
Sc³⁺ has no d electrons at all, and Zn²⁺ has ten, with both levels full. Either way no electron can jump, and no light is absorbed.

Hint
Colour needs a d electron that can jump to the upper level, and a free place there.

Worked solution
1. Scandium gives up all three electrons beyond argon: Sc³⁺ has no d electrons.
2. Zn²⁺ has ten d electrons: all five orbitals are full.
3. With no electron able to jump across Δ, there is no absorption and no colour.
4. Every ion in between has an electron that can jump, so they are coloured, even if pale.
Step 5 of 6
Open this step
Ammonia moves the band
Practice · Predict, then look
Question
Swap all six waters round Cu²⁺ for ammonia, and Δ grows by a quarter. Where does the absorption band move?

Correct answer
- Correct To shorter wavelengths
Setup, choices and feedback
The Scene at this step
Metal ion
Cu²⁺fixed
Ammonia ligands
0 of 6fixed
Zoom to the d orbitals
Test tubes
Choices
- Correct To shorter wavelengths
- Wrong To longer wavelengths
  Misconception: Thinks a bigger energy gap is matched by light of a longer wavelength.
  Feedback from the catalogue
  A photon’s energy grows as its wavelength gets shorter: a blue photon carries more energy than a red one. So a bigger gap absorbs shorter-wavelength light, and the band moves towards the blue.
- Wrong It stays put: the ion has not changed
  Feedback
  The ion is the same, but the ligands push harder on the d orbitals, and the gap between them grows.
Once the prediction is locked in, the Scene changes
Ammonia ligands
6 of 6fixed
The Scene then shows: 634.9 nm · Wavelength of the photon whose energy is Δ; NaN for d0 and d10/nodes/rack/outputs/gapWavelength
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The band moves from about 790 nm, past the red, to about 635 nm, in the orange-red. More visible light is absorbed, and the solution turns deep royal blue, a classic test for copper.

Worked solution
1. Ammonia pushes harder on the d orbitals than water does: Δ grows.
2. A bigger gap means a photon of higher energy.
3. A more energetic photon has a shorter wavelength: the band moves towards the blue.
Step 6 of 6
Open this step
A bigger gap
Practice · Calculate
Question
Read Δ for Cu²⁺ in water on the chart. Ammonia makes Δ a quarter bigger. What will Δ be when all six ligands are ammonia?

Correct answer
188.4 kJ/mol ± 3%
Setup, choices and feedback
The Scene at this step
Metal ion
Cu²⁺fixed
Ammonia ligands
0 of 6fixed
Zoom to the d orbitals
Test tubes
Accepted within
± 3%
Computed from the Scene at this step’s setting
The gap Δ for a mole of ions; NaN for d0 and d10/nodes/rack/outputs/splittingMolar
Any unit of the same quantity is accepted; it is converted before checking.
Feedback for a right answer
About 188 kJ/mol: 151 × 1.25. A photon of that energy is about 635 nm.

Hint
A quarter bigger: multiply by $1.25$ ⁠.

Worked solution
1. On the chart: Δ ≈ 151 kJ/mol for copper in water.
2. A quarter more: $151 \times 1.25 \approx 188$ ⁠.
3. Δ ≈ 188 kJ/mol.

Across the unit · 19 misconceptions

Misconception catalogue

Each common mistake this unit recognises, in a few words. Open one for what the learner reads when an answer matches it, and where it is asked.

Index

Inside an atom

Three particles

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

The atomic number

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

The mass number

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Writing an atom

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Finding an atom by its mass

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

Isotopes

One more neutron

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

Naming an isotope

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

The same chemistry

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

The natural mixture

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Reading the mean

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

Electron shells

Filling the shells

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution