Role of Quantum Numbers in Periodic Table

Periodic table is the most customised address book of elements. Elements are placed here in increasing order of their atomic number. Every element has got a specific place. As you know that every element has unique characteristics. So how is it possible to arrange them in rows and columns? You must have noticed the lengths of columns are different, and there are also a few incomplete rows and two rows are separately placed at the bottom of the table. Why there are 18 columns and 7 rows? In this post we will try to find some answers to these questions.

Rows in periodic table

Write the electronic configuration of first element of each row. Now find the principal quantum number for the outer most electron of each element. You will find “n” of the element is similar to the number of the row it belongs to.  

“s Block” 

When you look at the Periodic table, you will see there are two columns on the left side. Let’s write the electronic configuration of first two elements of the first column.

¹H = 1s¹

³Li = 1s², 2s¹

Notice the outer orbital of these elements; its “s” in both elements.

Now write the electronic configuration of first two elements of the second column.

⁴Be = 1s², 2s²

¹²Mg = 1s², 2s², 2p⁶, 3s²

Notice the outer orbital of these elements; its again “s” in both elements.

As you have noticed that, all the elements of these two columns have their last electron filled in “s” orbital. That’s why they are called “s Block” elements. Since “s” orbital can accommodate maximum 2 electrons that’s why “s block” comprises of two columns.

“p Block”

When you look on the right side of the table you will find 6 columns there. Now write the electronic configuration of at least first elements of each column.

In all these elements outer most electron is filled in the “p” orbital. That’s why these 6 columns are placed under “p Block”. You can guess why there are 6 columns in “p block”. Yes of course because “p” orbital can accommodate maximum 6 electrons. If you write the configuration of other elements of the same column you will find all of them have similar number of electrons in the “p” orbital. In other words, elements of the same column have same “l”, “m_l” and “m_s” quantum numbers.

“d Block”

You must have noticed the bridge of 10 columns in the periodic table. I know you guessed the right reason of the name of this block and reason behind the number of columns. Orbital d can accommodate 10 electrons that’s why it has 10 columns and each element has filled their outer most electron in “d” orbital.

Before you go to write the configuration, I want to tell you the (n+l) Rule. In the previous post about electronic configuration I have told you about energy order of the sub-shells.

Energy order of the sub-shells is as follows: s < p < d < f

When you compare the energy of sub-shells belonging to different orbits you will find

1s < 2s < 2p < 3s < 3p < 3d

The (n+l) rule, which I am going to explain, is about the energy of sub-shells. The sub-shell with higher (n+l) value has higher energy. Let’s check this rule in the energy order given above.

1s has n = 1, l = 0 so, (n+l) = 1

2s has n = 2, l = 0 so, (n+l) = 2

2p has n = 2, l = 1 so, (n+l) = 3

Yes this rule is working fine. Now workout yourself, the order of higher sub-shells 3d, 4s, 4p, 4d, and 4f.

3d has n = 3, l = 2 so, (n+l) = 5

4s has n = 4, l = 0 so, (n+l) = 4

So, the energy of 4s < energy of 3d.

4p has n = 4, l = 1 so, (n+l) = 5

There is tie between 3d and 4p. When there is a tie, the “Aufbau Principle” will decide which one has higher energy. According to this principle the orbit nearer to the nucleus has lower energy or in other words the orbit with higher “n” value has higher energy.

So, the energy of 4p > energy of 3d.

Now the complete energy order will be

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p

Like p block elements, elements of d block also has similar set of “l”, “m_l” and “m_s” quantum numbers.

Count the number of rows after which “d Block” starts. You will find that it starts from 4^th row. You can justify it from the energy order of sub-shells. Yes, because “d” sub-shell is not present in 1^st and 2^nd  orbit and electron cannot be filled in “3d” sub-shell before filling the “4s” sub-shell. That’s why row 1, 2 and 3 have a gap between “s block” and “p block”. And “d block” starts in 4^th row after “4s”.

“f Block”

It is shown as the extended part of the periodic table. In fact it is present between 6s and 5d but to maintain the symmetry of the periodic table it is placed separately. It has 14 columns because “f” sub-shell can accommodate maximum 14 electrons and the outer most electron of each element is filled in “f” orbital.

Do you remember, that 4^th orbit has 4sub-shells s, p, d and f? However in the energy order of sub-shells discussed above, we didn’t mention 4f sub-shell. Let’s find out its place in the energy order.

4f has n = 4, l = 3 so, (n+l) = 7

5p has n = 5, l = 1 so, (n+l) = 6

6s has n = 6, l = 0 so, (n+l) = 6

5d has n = 5, l = 2 so, (n+l) = 7

There is tie between 4f and 5d and 5p and 6s. In this situation, “Aufbau Principle” will be the tie breaker and 5d wins over 4f and 6s wins over 5p because greater “n” has greater energy.

Now the complete energy order will be

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p.

Position of ²He

After understanding the reasons behind the arrangement of blocks and the elements belonging to them, you will be able to guess the position of any element from its electronic configuration. When you write the configuration of ²He : 1s², you may place it in the “s Block” but, it is placed in “p Block”.

The arrangement of elements in perodic table also sets particular trends of their properties along the rows and columns such as size of atom, electonegativity, ionization enthalpy and electron gain enthalpy. These are known as periodic properties. In the coming posts I will discuss these properties and there trends one by one. 

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