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Electrons in shells

How electrons fill the shells around a nucleus, and why that arrangement gives an element its group and its period.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

By the end of this lesson you will be able to write the electron arrangement of any of the first twenty elements from its atomic number, filling the shells in order and checking the total, and read two things off that arrangement: the group, which is the outer-shell electron count, and the period, which is how many shells hold electrons. You will also be able to say where the simple filling rule stops being true, and why the periodic table has the shape it has.

2. What you already have

You can turn a symbol into a count of protons, neutrons and electrons, and you know that a neutral atom has as many electrons as protons. What you have not been told is where those electrons are. This lesson puts them somewhere, and that somewhere turns out to predict where the element sits on the periodic table.

3. Words for this lesson

4. Electrons go into shells, and the shells fill in order

Electrons are not scattered anywhere around the nucleus. They occupy shells, and the shells fill from the inside out, one before the next:

• the first shell holds up to $2$;
• the second holds up to $8$;
• the third holds up to $8$;
• the fourth begins after that.

To write the arrangement of an element, take its atomic number — which is also its electron count, because a neutral atom balances — and fill the shells in order until you run out.

Sodium has $11$ electrons. Two fill the first shell, eight fill the second, and one is left over and starts the third: $2, 8, 1$.

Two things fall straight out of that line, and they are what the periodic table is made of:

• The last number is the group. Sodium's outer shell holds one electron, and sodium is in group 1 — with lithium ($2, 1$) and potassium ($2, 8, 8, 1$), which have one outer electron too. That is why elements in a column behave alike: they have the same outer shell to work with.
• How many numbers there are is the period. Sodium's electrons occupy three shells, and sodium is in period 3. A new row of the table starts exactly when electrons start filling a new shell.

So the table is not a chart somebody decided on. It is what happens when you write the elements out in order and start a new line whenever a shell fills.

5. The first twenty, and the two numbers each one gives you

Reading down the table below, the pattern repeats rather than continues, and the repeat is the reason the periodic table has columns at all.

Lithium, sodium and potassium all end in a $1$, three rows apart, and all three are soft reactive metals that form ions with a single positive charge. Neon and argon both end in a full shell, and neither reacts with anything worth mentioning. The chemistry repeats because the outer shell repeats.

Helium is the exception to the group rule. It has two outer electrons and sits in group 8, not group 2, because its outer shell is full at two — and a full outer shell is what group 8 means. The rule group equals outer electrons is a shortcut that works everywhere else in this range.

Two ways of numbering the groups. This course numbers the main groups 1 to 8, so that the group number is the outer-shell electron count. A modern periodic table numbers all eighteen columns from 1 to 18, counting the ten short columns in the middle as well; in that numbering, group 7 is column 17 and group 8 is column 18. The two are the same columns counted differently, and nothing in this course turns on which you use.

6. The method, step by step, and how to check it

Count the electrons. For a neutral atom, the electron count is the atomic number.

Fill the first shell. Up to two electrons. Hydrogen has one; everything from helium on has two here.

Fill the second shell. Up to eight more.

Fill the third shell. Up to eight more, for the elements up to argon.

Put what is left in the fourth shell. Only potassium and calcium, in this course's range.

Read off the group and period. The last number is the outer shell and gives the group; the number of numbers gives the period.

Check the work. Do the numbers add back to the atomic number? Is every shell but the last one full — 2 in the first, 8 in each one after? Does the group you read off match the column the element is printed in? A line such as $2, 7, 2$ fails the second check at once, because the second shell was left with a space while the third was started.

7. Why each step is allowed

Taking the atomic number as the electron count is allowed because a neutral atom has equal positive and negative charge, and each proton's charge is balanced by one electron's.

Filling from the inside out is allowed because electrons nearer the nucleus are held more tightly and have lower energy. An atom in its ordinary state has each electron in the lowest-energy place still free, and the inner shells are lowest.

Reading the period as the number of shells is allowed because the table was laid out that way: a new row starts with the element whose electrons begin a new shell. Lithium starts row 2 with one electron in the second shell; sodium starts row 3 with one in the third.

Reading the group from the outer shell is allowed because elements in a column were grouped by their chemistry long before electrons were known, and the outer-shell count turned out to be exactly what they share.

8. Where this rule stops being true

The filling $2, 8, 8, 2$ is exact for the first twenty elements and wrong immediately afterwards.

The third shell can actually hold $18$, not $8$ — but the fourth shell starts filling before the third one finishes, which is why potassium and calcium go into the fourth shell with eight in the third rather than waiting. After calcium the third shell goes back and takes its remaining ten, and those ten elements are the short columns in the middle of the table: scandium through to zinc.

That is the real reason the periodic table has that odd shape, and it is also the reason this course stops the rule at calcium. Everything the next unit does — atomic radius, ionization energy, electronegativity — is worked out on elements where the simple filling holds, and where it does not, the course says so rather than quietly extending a rule past its edge.

9. In the world: why neon signs glow and argon fills light bulbs

The neon signs on the Las Vegas Strip and the argon inside an incandescent bulb both rely on the same fact from this lesson: a full outer shell. Neon is $2, 8$ and argon is $2, 8, 8$. Neither has an electron to give away easily or a space to take one, so neither reacts with the hot metal or glass around it.

That is exactly why argon fills light bulbs. A tungsten filament glowing at more than 4,000 degrees Fahrenheit would burn through in seconds in air, because oxygen ($2, 6$) is two electrons short of a full shell and reacts eagerly with hot metal. Argon, with its full outer shell, does nothing, and the filament lasts for a thousand hours.

In a neon sign, an electric current knocks electrons in the neon atoms up out of their shells for an instant. When they drop back, the atom gives off light of particular colors — red-orange for neon. The shells set which colors are possible, which is why each gas glows its own color. A sign maker who wants blue uses argon with a little mercury instead, a choice about electron arrangements made in a shop with glass tubing and a torch.

10. In the world: sodium in a salt shaker and a streetlight

Sodium ($2, 8, 1$) gives up its single outer electron so readily that it is never found free in nature, only as the ion in table salt. The orange glow of older American streetlights is sodium vapor, its outer electron dropping back into place.

11. Where this goes wrong

The period is read as a count of electrons. It is a count of shells. Sodium has eleven electrons and is in period 3, because eleven electrons need three shells to hold them.

The group is read as a count of shells. That is the period. The group is the last number of the arrangement, which is the outer shell alone.

A shell is started before the one inside it is full. There is no arrangement $2, 7, 2$. Electrons fill from the inside out, so an inner shell is either full or it is the last one.

The outer shell is thought to be where all the electrons that matter are — and also where the mass is. The first is true and the second is not: the electrons weigh almost nothing, and the mass is in the nucleus, which this lesson has not touched at all.

The group number is the number of electrons in the outer shell and the period number is how many shells there are. The table is not an arbitrary filing cabinet that elements were sorted into; it is what you get when you write the elements out in order of atomic number and start a new row every time a shell fills.

12. Writing chlorine, and reading its position off

1. Count the electrons to place.

   $Z = 17 \Rightarrow 17 \text{ electrons}$

   The electron count is the atomic number.

2. Fill the first two shells.

   $2 + 8 = 10$

   An inner shell is filled before the next is started.

3. Put the rest in the third shell.

   $17 - 10 = 7$

   Seven are left for the outer shell.

4. Write the arrangement.

   $2, 8, 7$

   Inside out.

5. Read the group and period.

   $\text{group } 7; \ \text{period } 3$

   One short of a full shell, so ready to take an electron.

13. Why sodium and potassium behave alike

1. Write sodium's arrangement.

   $11: \ 2, 8, 1$

   Fill in order.

2. Write potassium's arrangement.

   $19: \ 2, 8, 8, 1$

   The fourth shell starts after eight in the third.

3. Compare the periods.

   $3 \text{ shells against } 4$

   Different rows of the table.

4. Compare the outer shells.

   $1 \text{ outer electron each}$

   The outer shell is the only one chemistry reaches.

5. Name the shared group.

   $\text{group } 1$

   Same outer shell, same column.

6. Predict the ions.

   $\mathrm{Na^{+}}, \ \mathrm{K^{+}}$

   Each loses its single outer electron.

14. Calcium, the last element the rule covers

1. Count the electrons to place.

   $Z = 20$

   The atomic number.

2. Fill the first shell.

   $2$

   Up to two.

3. Fill the second shell.

   $8$

   Up to eight more.

4. Fill the third shell.

   $8$

   Up to eight, in this course's rule.

5. Put the rest in the fourth shell.

   $20 - 18 = 2$

   Two are left.

6. Check the total.

   $2 + 8 + 8 + 2 = 20$

   It adds back to the atomic number.

7. Read the group and period.

   $\text{group } 2; \ \text{period } 4$

   Two outer electrons, four shells in use.

15. Your turn: write the arrangement of sulfur, atomic number $16$, and give its group and period.

1. Fill the first two shells.

   $16 - 2 - 8 = 6$

   Fill from the inside out.

2. Write the arrangement.

   $2, 8, 6$

   The six go into the third shell.

3. Your turn: work this step out. Its working is at the end of the packet.

   Read the group and period.

16. Guided practice

Match each element to the arrangement of its electrons.

17. Guided practice

Complete the worked solution: an element has atomic number $14$. Its first shell holds two electrons and its second holds eight. Find the electrons in its third shell, its group and its period.

1. Find the electrons in the third shell.

   $(\text{atomic number}) - \text{ten} =$ _n

   Two and eight are already placed in the inner shells.

2. Read the group.

   $\text{group} =$ _g

   The group is the outer-shell electron count.

3. Read the period.

   $\text{period} =$ _p

   Electrons occupy three shells.

18. Guided practice

An atom of fluorine has its electrons arranged $$2, 7$$, and fluorine sits in period $2$ of the periodic table. Why?

• Its electrons occupy $2$ shells, and the period number is the number of shells in use.
• It has $9$ electrons altogether, and the period number counts the electrons.
• It has an outer-shell electron count of $7$, and that is what a period counts.

19. Practice

The electrons of an atom of chlorine are arranged $$2, 8, 7$$. Complete the sentence.

An atom arranged $2, 8, 7$ has an outer-shell electron count of _a, so it is in group _b; the number of shells in use is _c, so it is in period _d.

20. Practice

An electronics recycler in Phoenix sorts its scrap by element, and an assay of one batch names magnesium, atomic number $12$. How many electrons does one atom of it hold in its outer shell?

The answer: _a.

21. Somewhere new

A stockroom has been flooded and three bottles have lost their labels. The stock book is intact, and for each bottle it records only the electron arrangement of the element inside. Give the group and the period each element belongs to.

22. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

23. Test question

An atom of fluorine, $\mathrm{F}$, has atomic number $9$. Fill in how many electrons go into each shell. Write a zero for any shell that holds none.

24. What you can do now

You can turn an atomic number into an arrangement and an arrangement into a position on the table. Say out loud why lithium, sodium and potassium are in the same column, and why the answer has nothing to do with how many electrons they have altogether. Next: the periodic table itself, and the trends that follow from what you have just worked out.

Working for the steps left to you

15. Your turn: write the arrangement of sulfur, atomic number $16$, and give its group and period., step 3