by George Taniwaki

You would think that something as basic as the periodic table wouldn’t make the news. But recently two articles caught my attention. The Jun 2013 issue of Sci Amer (subscription required) points out that with the discovery of element 117 in 2010 (elements 1 through 116 and 118 had already been discovered), the periodic table has no gaps in it for the first time since it was first proposed in the 1860s. I found that pretty surprising. Of course, future discoveries of elements with higher atomic number may create new holes.

The article says that over 1,000 versions of the periodic table have been published. The arrangement that is most familiar was developed by Horace Groves Deming in 1923. An example table is shown below. It is color coded to indicate the date of discovery of each element. Note that four elements, shown in purple don’t have names yet.

PeriodicTable

Figure 1. Periodic table of elements showing era of discovery. Image courtesy of Wikipedia

The Deming chart starts with hydrogen (H) on the top left and helium (He) on the top right. The number of elements in each row tends to increase culminating in a separate block at the bottom for elements that start with lanthanum (La) and actinium (Ac). The elements in each column have similar chemical characteristics. For instance, the elements in the last column in each row are known as noble gases since they have high ionization energy potentials (the energy required to remove one electron). This makes it difficult, though not impossible, to make them react with other elements to form compounds.

IonizationEnergy

Figure 2. Ionization energy to remove one electron from each element. Image courtesy of Wikipedia

Another way to lay out the elements in a table is to group them by their quantum electron structure rather than by their chemical behavior. One example is the Janet left-step table. It was developed by the chemist Charles Janet in 1928. It moves helium to the column next to hydrogen and moves the first two columns to the end of the table. Each element falls into a block. The lanthanum and actinium row of elements are given their place in the main table, rather than having to sit at the children’s table.

PeriodicTableJanetLeftStep

Figure 3. Janet left-step periodic table of elements. Image by George Taniwaki

Electron quantum numbers

Each row in the Janet left-step table indicates increasing electron energy level. This is represented by the integer n, called the principal quantum number. The first eight levels are named K, L, M, N, O, P, Q, and R respectively.

The number of blocks in each row is represented by the integer , which must have a value of < ((n+1)/2 ) and is called the azimuthal quantum number. The first five blocks are named s, p, d, f, and g respectively.

My version of the Janet left-step table above color codes each element to show which block new electrons are added, f (green), d (blue), p (yellow). and s (red). Note that there are exceptions to the block ordering. (An explanation is beyond the scope of this blog post.)

The number of orbitals in each new block is larger than the block to the right of it. Specifically, each block contains m pairs of cells = (2 * –1) cells, where m is an integer called the magnetic quantum number. You can predict that the g block in the next row of the periodic table will contain 9 pairs (18 total) cells.

Besides n,  ℓ, and m, electrons have a fourth quantum property called spin which is represented by s, an integer that can have a value of either +1 or –1. No two electrons in an atom can have the same 4 quantum values.

The images below show the orbitals for a single electron in a hydrogen atom as energy increases. Note there is a single s orbital, 3 p orbitals, 5 d orbitals, and 7 f orbitals. Each orbital can hold two electrons with spin +1 and -1, which explains why the s, p, d, and f blocks hold 2, 6, 10, and 14 electrons respectively.

Single_electron_orbitals

Figure 4. Single electron orbitals. Image courtesy of Wikimedia Commons

Order in which electron orbitals fill

Each electron orbital has a different energy level. Orbitals with larger primary quantum number and larger azimuthal quantum number have higher energy than those with lower values. Electrons tend to fill the orbitals in what is called the Madelung rule which states that on average, orbitals with higher value of n + have higher energy. For orbitals with the same value of n +, those with higher value of n have higher energy. Thus, the order in which orbitals fill is a diagonal array as shown in the table below. This describes the layout of the elements in the Janet left-step table.

ℓ=1
s
ℓ=2
p
ℓ=3
d
ℓ=4
f
ℓ=5
g
n=1
K
1
1s
n=2
L
2
2s
3
2p
n=3
M
4
3s
5
3p
7
3d
n=4
N
6
4s
8
4p
10
4d
13
4f
n=5
O
9
5s
11
5p
14
5d
17
5f
n=6
P
12
6s
15
6p
18
6d
n=7
Q
16
7s
19
7p
n=8
R
20
8s

A pretty periodic table

In other periodic table news, the Aug 2013 issue of Pop Sci features a periodic table drawn by Alison Haigh, a London-based graphic designer. The article calls it beautiful and easy-to-read. I agree that it is beautiful. I don’t agree that it is easy-to-read or useful.

PeriodicTableAlisonHaigh

Figure 5. Periodic table without text. Image courtesy of Alison Haigh

First, showing both the cells and the dots is redundant. Just showing one or the other would be sufficient to convey the meaning. That’s because a periodic table is laid out in atomic number order. Thus, to find the atomic number of an element you can just count the number of cells from the top left or count the number of dots in the selected cell. To find which orbitals are filled for an element, you can see which row and column the element is in, or you can inspect the dot pattern in the selected cell.

The dots in each cell are arranged in an unusual order. They are grouped in concentric circles in order of their principal quantum number. The innermost circle has 2 dots, followed by rings containing 8, 18, 32, 32, 18, and 2 dots respectively. This means the dots are not arranged in the order that the electron orbitals are filled. This is a bit confusing.

Further, this arrangement only allows for up to 112 electrons, which corresponds to the element copernicium (Cn). The outer rings do not have room for additional dots to represent electrons for heavier elements that have already been discovered or predicted by quantum theory.

Finally, one of the most important uses of the periodic table is to help recall the names, abbreviations, and atomic number of the elements. There are no labels in this table. And counting the dots, or counting the number of cells to figure out the atomic number is tedious.

A modified version of Ms. Haigh’s periodic table is shown below. The elements are laid out in a spiral that follows the Janet left-step periodic table. Cells are color coded to highlight the s, p, d, and f blocks. Each cell is labeled with the atomic number and abbreviation of the element. It’s pretty, I guess; it looks like one of those eye tests for color blindness. But the layout is still not as useful as a standard periodic table.

PeriodicTableHaigh2

Figure 6. Periodic table based on Alison Haigh design. Image by George Taniwaki

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In 8th grade science class we were required to memorize the names of all the elements and their symbols. Do teachers make their students do that today? It seems rather pointless. How often do you use ruthenium (Rh)? There were only 98 named elements back when I was in school, so memorization was easier than it would be today where there are 114 and counting. Incidentally, based on that statement, can you can guess how old I am?

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