Metal atoms are assumed to be closely packed spheres in the metallic crystal. These metal atom spheres are considered to touch one another in the crystal. One half of the inter nuclear distance between the two closest metal atoms in the metallic crystal is called metallic radius.

Metallic radius > Covalent radius

For example - Metallic radius and covalent radius of potassium are `2.3` `-` and `2.03-` respectively.

The molecules of non-metal atoms are generally gases. On cooling, the gaseous state changes to solid state.

In the solid state, the non-metallic elements usually exist as aggregations of molecules and are held together by Van der Waal forces. One half of the distance between the nuclei of two adjacent atoms belonging to two neighbouring molecules of a compound in the solid state is called Van der Waal's radius.

It may also be defined as half of the inter nuclear distance of two non-bonded neighbouring atoms of two adjacent molecules.

See fig.1.

Vander Waal's radius > Metallic radius > Covalent radius

See fig.2.

The Vander Waal's radius and Covalent radius of Chlorine atom are `1.80 -` and `0.99 -` respectively.

A neutural atom changes to "cation by the Ioss of one or more electrons and to an anion by the gain of one or more electrons. The number of charge on cation and anion is equal to the number of electrons lost or gained respectively. The ionic radii of the ions present in an ionic crystal may be calculated from the inter-nuclear distance between the two ions.

i) `text(Radius of a Cation)` : Radius of a cation is invariably smaller than that of the corresponding neutral atom

`quad quad quad quad Na quad Na^(+)`

Number of `e^(-)= 11 quad 10`

Number of `p = 11 quad 11`

`1 s^2 quad 2s^2 quad 2p^6 quad 3s^1 quad 1 s^2 quad 2s^2 quad 2p^6`

`text(Reasons)` :

a) The effective nuclear charge increases. For example in `Na` atom `11` electrons are attracted by `11` protons and in `Na^(+)`, `10` electrons are attracted by `11` protons. Thus in the formation of cation number of electrons decreases and nuclear charge remains the same.

b) Generally the formation of cation results in the removal of the whole outer shell.

c) Inter electronic repulsion decreases. The inter electronic repulsion in `Na` is among `11e^(-)` and in `Na^(+)` among `10e^(-)`

ii) `text(Radius of an anion)` : Radius of an anion is invariably bigger than that of the corresponding atom.

`quad quad quad quad quad Cl quad Cl^(-)`

Number of `e^(-) = 17 quad 18`

Number of `p = 17 quad 17`


`text(Reasons)` :

a) The effective nuclear charge decrease in the formation of anion. Thus the electrostatic force of attraction between the nucleus and the outer electrons decreases and the size of the anion increases.

b) Inter electronic repulsion increases.

iii) `text(lso-electronic series)` : A series of atoms, ions and molecules in which each species contains same number of electrons but different nuclear charge is called isoelectronic series.

`quad quad quad quad quad quadN^(3-)quad O^(2-) quad F^(-) quad Ne quad Na^(+) quad Mg^(2+)`

Number of `e^(-) quad = 10 quad 10 quad 10 quad 10 quad 10 quad 10`

Number of `p = 7 quad 8 quad 9 quad 10 quad 11 quad 12`

a) Number of electrons is same.

b) Number of protons is increasing

c) So the effective nuclear charge is increasing and atomic size is decreasing. In an iso-electronic series atomic size decreases with the increase of charge.

Some of the examples of iso-electronic series are as under

i) `S^(2-), Cl, K^(+), Ca^(2+), Sc^(3+)`

ii) `SO_2, NO_3^(-), CO_3^(2-)`

iii) `N_2, CO, CN^(-)`

iv) `NH_3, H_3O^(+)`

a) In a period from left to right effective nuclear charge increases because the next electron fills in the same shell. So, the atomic size decreases. For example the covalent radii of second period elements in `-` are as follows -

`Li quad Be quad B quad C quad N quad O quad F`

`1.23 quad 0.89 quad 0.80 quad 0.77 quad 0.74 quad 0.73 quad 0.72`

b) In a group moving from top to bottom the number of shells increases. So the atomic size increases. Although the effective nuclear charge increases but its effect is negligible in comparison to the effect of increasing number of shells. For example the covalent radii of `IA` group elements in `-` are as follows -

`Li quad Na quad K quad Rb quad Cs`

`1.23 quad 1.57 quad 2.03 quad 2.16 quad 2.35`

The atomic radius of inert gas (zero group) is shown largest in a period because of its Van der Waal's radius which is generally larger than the covalent radius. The Van der Waal's radius of inert gases also increases in moving from top to bottom in a group.

There are three series of transition elements -

`3d - Sc (21)` to `Zn (30)`

`4d - Y (39)` to `Cd (48)`

`5d - La (57), Hf (72)` to `Hg (80)`

a) From left to right in a period

i) The atomic size decreases due to the increase in effective nuclear charge.

ii) In transition elements, electrons are filled in the (`n-1`)`d` orbitals. These (`n-1`)`d` electrons screen the `ns` electrons from the nucleus. So the force of attraction between the `ns` electrons and the nucleus decreases.

This effect of (`n-1`)`d` electrons over `ns` electrons is called shielding effect or screening effect. The atomic size increases due to shielding effect and balance the decrease in size due to increase in nuclear charge to about `80%`.

iii) Thus moving from left to right in a period, there is a very small decrease in size and it may be considered that size almost remains the same.

iv) In the first transition series the atomic size slightly decreases from `Sc` to `Mn` because effect of effective nuclear charge is stronger than the shielding effect. The atomic size from the `Fe` to `Ni` almost remains the same because both the effects balance each other. The atomic size from `Cu` to `Zn` slightly increases because shielding effect is more than effective nuclear charge due to `d^10` structure of `Cu` and `Zn`. The atomic radii of the elements of `3d` transition series are as under :

`Sc quad Ti quad V quad Cr quad Mn quad Fe quad Co quad Ni quad Cu quad Zn`

`1.44 quad 1.32 quad 1.22 quad 1.18 quad 1.17 quad 1.1 7 quad 1.16 quad 1.15 quad 1.17 quad 1.25`

As we move along the lanthanide series, there is a decrease in atomic as well as ionic radius. The decrease in size is regular in ions but not so regular in atoms. There is a significant drop in atomic size after `Ill` `B` group as we move from left to right in periods `6` & `7`. This is called lanthanide contraction. The atomic radii in `-` are as under :

`La quad Ce quad Pr quad Nd quad Pm quad Sm quad Eu quad Gd`

`1.88 quad 1.82 quad 1.83 quad 1.82 quad 1.81 quad 1.80 quad 2.04 quad 1.80`

`Tb quad Dy quad Ho quad Er quad Tm quad Yb quad Lu`

`1.78 quad 1.77 quad 1.76 quad 1.75 quad 1.74 quad 1.94 quad 1.73`

There are two peaks one at `Eu` (`63`) and other at `Yb` (`70`). This is due to the difference in metallic bonding. Except `Eu` and `Yb` other lanthanides contribute three electrons in metallic bond formation. These two atoms contribute two electrons in the bond formation leaving behind half filled and completely filled `4f`-orbitals respectively.

`text(Cause of Lanthanide contraction)` : In lanthanides the additional electron enters into (`n-2`)`f`-orbital. The mutual shielding effect of (`n-2`)`f` electrons is very little because the shape of `f`-subshell is very much diffused. Thus the effective nuclear charge increases in comparison to the mutual shielding effect of (`n-2`) `f` electrons. The outer electrons are attracted more by the nucleus. Consequently the atomic and ionic radii decreases from `La` (`57`) to `Lu` (`71`).

This type of contraction also occurs in actinides. The jump in contraction between the consecutive elements in the actinides is greater than lanthanides. This is due to the lesser shielding of `5f`-electrons which are therefore pulled more strongly by the nucleus.

`text(In a group)`

i) The atomic radius of elements increases moving from first transition series (`3d`) to second transition series (`4d`). This is due to the increase in number of shells with the increase in atomic number.

ii) The atomic radii of second (`4d`) and third (`5d`) transition series in a group is almost same except `Y`(`39`) and `La` (`57`).

In third transition series, there are fourteen lanthanides in between `La` (`57`) of `III B` and `Hf` (`72`) of `IV B` groups, so the atomic radius of `Hf` (`72`) decreases much due to lanthanide contraction in lanthanides. The difference in the nuclear charge in the elements of a group in first and second transition series is `+18` units while this difference in second and third transition series is `+32` units except `Y` (`39`) `->` `La` (`57`). Due to the increase of `+32` units in the nuclear charge there is a sizable decrease in the atomic radius which balances the increase in size due to the increase in number of shells.

So in a group moving from second to third transition series, the atomic radii of the elements almost remain the same except `III B`. The difference is about `0.02 -`.