[harini_5]

While teaching about PERIODICITY my teacher explained the trends of various properties. While talking about DENSITY he told us that the potassium is lighter than sodium because increase in atomic volume overweighs the increase in atomic mass. But, why is there a larger increase in atomic volume in this pair alone and not in others?
In atomic structure I’ve that as the energy level goes on increasing, the differences between successive energy levels decrease. Doesn’t this mean that the exception I’ve stated above should occur with Lithium and sodium and not with sodium and potassium?

[Alpha-Omega]

I perceive the question to be phrased “awkwardly.”  You seem to be looking for a trend where there is an exception (e.g., applying the EXCEPTION-where the density of potassium is less than the density of sodium to the species lithium and sodium).  I am going to attempt to answer it this way: 

Although there are trends in the periodic table; and, indeed it was designed based on trends, there are exceptions.  Exceptions are unique.  They are not the norm.  When encountered you must understand that they exist and are there. 

There is a trend in increasing density down the groups in the periodic table.

There is an exception in the density trend between sodium and potassium. The exception is that although the atomic mass increases and the number of protons increase for potassium, its density is less than that for sodium.

Basically, as you go down a group the elements are heavier because they contain more protons and neutrons in their nuclei. But working against this is the fact that the increased nuclear charge tends to pull all the electrons closer, resulting in a smaller atomic radius and hence a higher density.

Density down a group generally increases, with the notable exception of potassium being less dense than sodium.

Basically, in the case of sodium and potassium the increase in shell size outweighs the pull of the core on the outer shell electron and so potassium is less dense than sodium.  In the sodium/potassium pair this effect counteracts the effect of increased nuclear mass.

In atomic structure I’ve that as the energy level goes on increasing, the differences between successive energy levels decrease. Doesn’t this mean that the exception I’ve stated above should occur with Lithium and sodium and not with sodium and potassium?

I am not sure what you are driving at in the above statement.

The electron configurations for lithium, sodium, and potassium are as follows:

Lithium:  Electron Configuration:  1s² 2s¹  or   [He]2s¹
Sodium:  Electron Configuration:  1s² 2s² 2p⁶ 3s¹   or    [Ne]3s¹
Potassium:  Electron Configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ or [Ar]4s¹ (note that K has a 3d shell available for bonding that lithium and sodium do not have).

The 4s energy level is higher for potassium (n = 4) than the 3s energy level (n = 3) for potassium.  If you do the Slater calculation for the 4s and 3d levels for potassium you can see why the electron prefers to fill the 4s shell as opposed to the 3d.

In this example apply Slater’s Rules to determine the most likely electron configuration:

[Ar]4s¹ Z_eff for the s  = 19 – [10 x 1]- [8 x .85] = 2.20
[Ar]3d¹ Z_eff for the d electron = 19 – [18 x 1] = 1.00

As expected based on explanations in text books the first configuration is the more stable configuration. The last electron is held more tightly as an s electron than a d electron. Another way to look at it is that a 3d-electron is  shielded more effectively than a 4s-electron.

[AWK]

The same difference concerns magnesium and calcium but this is rarely discussed because of different crystal structures of these metals (though with exactly the same packing coefficient)

[Alpha-Omega]

And perhaps cesium and francium.

It is quite difficult to come up with a simple explanation for this, because the density depends on two factors, both of which are changing as you go down the Group.

All of these metals have their atoms packed in the same way, so all you have to consider is how many atoms you can pack in a given volume, and what the mass of the individual atoms is. How many you can pack depends, of course, on their volume - and their volume, in turn, depends on their atomic radius.

As you go down the Group, the atomic radius increases, and so the volume of the atoms increases as well. That means that you can't pack as many sodium atoms into a given volume as you can lithium atoms. 1 cm³ of sodium will contain fewer atoms than the same  1cm³ volume of lithium, but each atom will weigh more.

Density is the ratio of mass to volume. Both size and mass increase down a column of the periodic table. However, since the size of atoms does not increase as dramatically as the mass (recall all atoms are of roughly comparable size) density should increase down the alkali metal column. The facts are that while the atomic mass of cesium is 19 times larger than that of lithium (133 vs 7 amu), the radius of Cs is only about double that of Li (2.3 vs 1.2 Angstroms).

You can determine the density of sodium if you know lithium's density and have figures for relative atomic mass and atomic radius - and then apply this all the rest of the way down the Group. You will find that the density is inversely proportional to the volumes of the atoms and directly proportional to their masses.

Generally speaking, as you go down the Group, the mass of the atoms increases. That means that a particular number of sodium atoms will weigh more than the same number of lithium atoms.