Valence electrons are those electrons that reside in the outermost shell surrounding an atomic nucleus. Valence electrons are of crucial importance because they lend deep insight into an element’s chemical properties: whether it is electronegative or electropositive in nature, or they indicate the bond order of a chemical compound – the number of bonds that can be formed between two atoms. Since covalent bonds are formed by the sharing of electrons present in the final shell, the number indicates how many bonds are permitted to form.

The most palpable method would be to refer to an element’s atomic configuration and simply count the electrons in the outermost shell. However, this would be an extremely tedious chore, since we might have to rummage through textbooks to seek out configurations with which we’re not familiar.

However, there’s no need to fret, as there’s a much simpler manner of finding this coveted number. This is a more generalized approach that only requires summoning one small resplendent rectangular sheet of paper — the periodic table. To find the number of valence electrons of an element, we must only refer to the periodic table and seek the element’s position within it.

The periodic table is a neat arrangement of all the elements we have discovered to this point. The elements are arranged from left to right in ascending order of their atomic numbers, or the number of protons or electrons they contain.

The elements are divided into four categories: main group elements, transition elements, lanthanides and actinides. The latter two are also known as inner transition elements. The table contains 18 columns in total, formally known as groups, as well as rows, formally known as periods. There are 7 rows in the subtable above and 2 rows distinguishing the rarer elements below. The transition elements form a bridge or perpetuate the transition between the elements in Groups 2 and 13.

As we move down a group, the number of valence electrons remains the same, even though the number of shells increases. While valence electrons across a period incrementally climb by one, the number of shells remaining the same. The period number (row number, to remind you) in which an element can be found indicates the number of shells encircling its nucleus.

So, what is the significance of the group number?

While the period number indicates the number of shells, the group number indicates the number of valence electrons in the outermost shell. Specifically, the number in the ones’ place. However, this is only true for the main group elements – the elements inhabiting groups 1-2 and 13-18.

The rule is inapplicable to the transition and inner transition elements (we’ll get to the reason in a minute). For instance, Sodium (Na) resides in Period 3, Group 1, which implies that it has 3 shells and a single electron in its valence shell.

Or, you can consider chlorine in Group 17. Accordingly, in order to determine its valence electrons, we must only seek the number in its ones’ place: 7. As expected, that is exactly the number of electrons in its valence shell.

accompanied the laborious search for individual atomic configurations.

Now what about the valence electrons of the elements in between? Obviously, we can’t forget the lanthanides and actinides…

Transition elements are not much different from metals that go shoulder to shoulder in the main group elements. They appear like metals, they are malleable, ductile and can conduct both heat and electricity. The fact that the best two conductors – Copper (Cu) and Aluminum (Al) – are transition metals shows the extent to which their properties overlap.

However, they do not duplicate the results that we derived from the method above. One cannot enumerate their valence electrons by simply referring to their group number. This boils down to the way electrons occupy shells in transition elements.

To understand this exception, we must understand how electrons occupy shells in any element. First, however, we must unlearn the high school method of filling shells around an atomic nucleus: remember 2..8..8..18 and so on? Well, there’s a reason why we distribute electrons in this particular fashion.

The solar system analogy describing the arrangement of electrons around an atom is completely false. It should be immediately eliminated, but because it alleviates the difficulty that accompanies the exposition of the actual model, high school textbooks are replete with them.

Electrons do not occupy rigid shells around their nucleus. In fact, their location around a nucleus is highly uncertain. They can only occupy distinct energy levels around a nucleus. They’re most probable to be found there. The levels are technically known as quantum states and are denoted by what are called quantum numbers (n).

Now, the next sentence might sound hypocritical, but quantum numbers can be thought of as our good ol’ shells, but with sub-shells now, which are technically known as orbitals (s,p,d,f). Regardless of the falsity of this account, it fares quite well for a crash course such as this one.

There’s a rule that restricts the number of electrons that a sub-shell can accommodate: s-2, p-6, d-10 and f-14. If this wasn’t enough, adding to the delirium, the shells can only be filled in a specific order given below. Let’s call it the rule.

The electrons must be filled from left to right in this exact order only.

If we were to distribute electrons unconsciously with respect to how the sub-shells are lined up, as shown in the figure above, Calcium (Ca) with atomic number 20 would have the configuration 2,8,10 (2, 2+6, 2+6+2). Any high school chemistry textbook will tell you that this isn’t correct, as the precise configuration is 2,8,8,2.

However, because we must abide by the rule, we observe that 4s must be filled before 3d, such that there are now 8 in the 3rd shell and 2 in the 4th making the configuration: 2,8,8,2. Voila! As Richard Feynman would cheerfully exclaim: The pleasure of finding things out! Sadly, the joy is only half-lived — the reason for the rule itself, this apparent absurdity, is beyond the scope of this article.

Okay, so now that we know how shells are filled, we can move further to find the number of valence electrons in the transition elements. Consider Scandium (Sc) with its atomic number of 21. Filling the electrons according to our rule, we observe that the 21st electron occupies the 3d sub-shell. However, as the previously filled 4th shell (4s) has 2 electrons and is apparently the outermost shell, the number of valence electrons is 2.

Similarly, every transition element in the 4th period must have 2 valence electrons. The reason being that even though 3d gets filled ahead of 4s, the two electrons situated in the 4th shell are the inhabitants of the outermost shell and rightfully deserve the designation of valence electrons.

In fact, this is true for transition elements in every period. Consider Gold (Au), located in the 6th period (row) and the 11th group (column). In the process of fillings its shells, one can realize that the stuffing of 5d is followed by the stuffing of 6s. And because the 6th shell resides above the 5th, the number of valence electrons is… *drumroll*… 2!

However, this is how electrons would ideally line up. The energy differences between these shells are minuscule and electrons (or Nature, for that matter) covets stability more than anything else. An electron would happily make a leap to an adjacent shell of relatively equivalent energy to attain a more stable configuration.

A good example is the fickle configuration of a Copper (Cu) atom. Copper has 29 electrons in total, so the rearmost electrons are lined up as …4s^2-3d^9. For Copper, the configuration is a little unsettling — a more stable configuration would be to have 10 electrons in the 3d shell, and this is exactly what we observe! Because the energies of the shells are comparable, an electron from 4s makes a leap to 3d to fulfill a stable configuration. The number of valence electrons is now 1!

A number of elements amongst the transition elements portray this oddity. This is also observed in the inner transition elements due to the comparable energy levels of f, d and s shells. Therefore, in conclusion, the number of valence electrons for transition and inner transition elements varies in an unpredictable manner.

Although one can still predict the number of valence electrons for the transition elements – and 2 is what most of them would agree upon – this sort of prediction cannot be emulated for the inner transition elements. The difficulty is compounded as the locations of electrons themselves are highly ambiguous.

The capricious behavior of their valence electrons, interminably quivering and hopping in indecision, deny any attempt to obtain a singular stable configuration — predicting then the number of valence electrons is near to impossible!

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