8 junio, 2024

Quantum table: what it is, characteristics, what it is for, uses

What is the quantum table?

The quantum table It is a way of organizing the chemical elements, designed to easily determine the set of quantum numbers that characterizes each of them.

Scientists have found that in the nature of all elements, there are certain patterns. Among these patterns are quantum numbers, four simple numbers that describe the electronic configuration of each element.

Quantum numbers arise naturally from the quantum mechanical model of the atom and are denoted by letters: n, ℓ, mℓ, and s. They describe the energy state of the electrons in the atom of each chemical element.

Through the traditional periodic table, and some additional tools, it is possible to have the electronic configuration of the atom of any element. The advantage of the quantum table is that the elements are arranged in such a way that their quantum numbers are immediately visible, without the need to do numerous separate calculations.

Quantum Table Features

There are various designs of quantum tables. The model shown in the figure above contains:

A header with four rows, with the values ​​of the four quantum numbers, n, ℓ, mys, plus a fifth row in yellow, which corresponds to the number of electrons in the outermost orbital.
The body of the table, consisting of a grid containing the chemical element symbol, beginning with hydrogen, in the penultimate column on the right, followed by helium, and so on. The number below represents the number of electrons in the atom in its ground state.
At the bottom, in the green row, there are four classes to organize the elements: the s, p, d and f orbitals (from left to right).
Lastly, below the row of orbitals is the family. Each column is a family, numbered from 1 to 32. For example, families 1st and 2a belong to class s, families 3rd to 8th belong to class p, and so on.

What is the quantum table for?

The quantum table is used to find the set of quantum numbers that characterizes an electron in the atom. Normally, these electrons will be those of the outermost layer, since they are the ones that define the chemical behavior of the element.

How is the quantum table used?

The quantum table makes it easy to find the quantum numbers of the electrons in the outermost shell of the atom.

Example 1

To illustrate the procedure, the aluminum element, whose symbol is Al, is taken as an example. The first step is to locate it in the quantum table, marking it with a Red circle:

Step 1: find n

After locating the element in the table, you have to scroll through that same row and color, to the right, until you reach the orange column, following the path of the green arrow shown in the image.

The arrow points to the box marked with the number 3, which is the principal quantum number n:

n=3

Step 2: find

To determine the secondary quantum number, follow the blue vertical arrow, which indicates:

ℓ = 1.

Step 3: find m

The outer electron of aluminum is in the family of the p subshell, as can be read in the bottom green row, which the pink arrow points to.

Also, the number of electrons in the last shell is read in the yellow header row. In the case of aluminum there is 1 electron (highlighted in the purple square), which is the reference one. Combining the previous results, the configuration of the last layer results:

3p1

It is known that a p shell admits a maximum of 6 electrons. And the number m takes some of the integer values ​​− ℓ , (− ℓ+1), …0, … (+ℓ −1), +ℓ.

Since in this case ℓ = 1, then m can be −1, 0, 1.

These numbers appear in the header row corresponding to am (see in the image the horizontal arrow blue). The following table serves as a guide to know which is the value of m to choose, depending on the case:

Since the last shell of aluminum has 1 electron, the magnetic quantum number corresponds

m = 1.

Step 4: find yes

The spin number s only has two values: +½ or – ½. In the box above, if the arrow points up, choose s = +½ and if it points down, then s = – ½. In the case of aluminum, the 1 electron points up, therefore:

s = + ½.

Summarizing, the quantum numbers of the electron in the outermost shell of aluminum Al are:

n=3; ℓ = 1; m = 1, s = +½

Example 2 (exceptional cases)

Silver Ag, and about twenty other elements, are exceptional cases, so care must be taken when using the quantum table with them.

If the previous procedure is repeated, the 4d9 would be obtained for Ag as the last sublevel.

This is because the predicted configuration of silver, by Madelung’s rule, is:

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d9

In practice, however, Ag doesn’t exactly follow this setup, nor do any of the other elements whose last predicted layer is 4d9, such as copper and gold, among others (check the internet for a full list of elements that don’t). follow Madelung’s rule.

The actual configuration of Ag is:

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1 4d10

In which an electron from the 5s2 shell jumped to the 4d9 shell to complete it. This increases the stability of the atom. Therefore, the last sublevel is really:

5s1

And their quantum numbers would be those corresponding to the element Rb, shown in a purple box, with orange arrows indicating the remaining numbers:

n=5; ℓ = 0; m = 0; yes = +½

Reviewing the periodic table, it is indeed seen that Ag is in period 5, a characteristic determined by the principal quantum number n.

Differences with the periodic table

Both tables are two ways of organizing the chemical elements according to the characteristics of their atoms:

-In the periodic table, elements found in the same column have similar chemical properties. For example, start with the alkali metals column on the left and end with the noble gases column on the right. While in the rows are the elements with the same higher level of energy.

-The quantum table has a staggered arrangement, designed according to the filling rules. For this reason, the steps must be followed to obtain the main quantum number, except in the case of exceptions such as silver, in the example of the previous section. The element families in this table are related through the higher orbital, in s, p, c or f.

References

Chang, R. 2013. Chemistry. 11th Edition. McGraw Hill Education.
Electronic configuration. Electronic configuration and quantum numbers. Recovered from: configuracionelectronica.com.
Chemistry Handbook. Recovered from: dcb.ingenieria.unam.mx.
official chemistry. How to easily calculate quantum numbers. Recovered from: quimicaoficial.com
triplelink. Exceptions to the Madelung rule in the electronic configuration of chemical elements. Recovered from: triplenlace.com.

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