Atomic Radius

Periodic Properties of Class 11

The radius of an atom may be taken as the distance between atomic nucleus and the outermost shell of electrons of the atom. The size of atom is very important because many physical and chemical properties of the atom are related to it. According to the Heisenberg's uncertainty principle the position of a moving electron can not be accurately determined. So the distance between the nucleus and the outermost electron is uncertain. Atomic radius can be determined indirectly from the inter-nuclear distance between the two atoms in a gaseous diatomic molecule. This inter-nuclear distance between the two atoms is called bond length. Different types of atomic radii are discussed below.

Covalent radius: One half of the distance between the nuclei (inter-nuclear distance) of two covalently bonded atoms in a homo-diatomic molecule is called the covalent radius of that atom. The covalent bond must be single covalent bond. The covalent radius (rA) of atom A in a molecule A2 may be given as –

Atomic Radius

i.e. the distance between the nuclei of the two single covalently bonded atoms in a homo-diatomic molecule is equal to the sum of covalent radii of both the atoms.

dA-A = rA+rA

In a hetero-diatomic molecule AB where the electronegativity of atoms A and B are different, the experimental values of inter-nuclear distance dA-B is less than the theoretical values (rA+rB). According to Schomaker and Stevenson (1941) –

DA-B = rA + rB – 0.09 Δx

Where Δx is the difference of electronegativities of the atoms of A and B

According to Pauling – If the electronegativities of the two atoms A and B are xA and xB respectively then

DA-B = rA + rB – (C1xA – C2xB)

C1 and C2 are the Stevenson's coefficients for atoms A and B respectively.

Metallic radius: 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 internuclear 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 Å and 2.03Å respectively.

  • Van der Waal's Radius or Collision radius: The molecules of non metal atoms are generally gaseous. On cooling, the gaseous state changes to liquid which is followed solid state on further cooling. In the solid state, the non metallic elements usually exist as aggregations of molecules are held together by Van-der Wall forces. One half of the distance between the nuclei of two adjacent atoms belonging to two neighbouring molecules of an element 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.

Atomic Radius

Vander Waal's radius > Metallic radius> Covalent radius

The Vander Waal's radius and covalent radius of chlorine atom are 1.80Å and 0.99Å respectively

  • Ionic Radius: A neutral atom changes to a cation by the loss 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 internuclear distance between the two ions

(a) Radius of a Cation–Radius of a cation is invariably smaller than that of the corresponding neutral atom

NaNa+

Number of e- = 1110

Number of p =1111

1s22s22p63s11s22s22p63s0

Reasons

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.

Generally the formation of cation results in the removal of the whole outer shell due to which interelectronic repulsion decreases. The interelectronic repulsion in Na is among 11e- and in Na+ among 10e-

(b) Radius of an anion – Radius of an anion is invariably bigger than that of the corresponding atom

ClCl_

Number of e- =1718

Number of p = 1717

Reasons

The effective nuclear charge decreases 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.

Interelectronic repulsion increases due to which expansion of electron cloud takes place

Isoelectronic species:

A series of atoms, ions and molecules in which each species contains same number of electrons but different nuclear charge is called isoelectronic series

N3O2-F- Ne Na+ Mg2+

Number of e- 101010101010

Number of p789101112

In isoelectronic series atomic radii decreases, nuclear charge increases as

(i) Number of electrons is same.

(ii) Number of protons is increasing

(iii) So the effective nuclear charge is increasing and atomic size is decreasing. In an isoelectronic series atomic size decreases with the increase of effective nuclear charge.

Some of the examples of isoelectronic series are as under

S2-, Cl-,K+, Ca2+, Sc3+

SO2, NO3-, CO2-3

N2, CO, CN-

NH3, H3O+

PERIODICITY IN ATOMIC RADIUS AND IONIC RADIUS

For normal elements

(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 Å are as follows –

LiBeBCNOF

1.230.890.800.770.740.740.72

(b) In a group, from top to bottom the number of shells increases. So the atomic size increases. Although the 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 Å are as follows –

LiNaKRbCs

1.231.572.032.162.35

  • The atomic radius of inert gas (zero group) is shown largest in a period because of its Vander Waal's radius which is generally larger than the covalent radius. The Vander Waal's radius of inert gases also increases in moving from top to bottom in a group.
  • For transition elements – There are four series of transition elements

3d – Sc (21) to Zn (30)

4d – Y (39) to Cd (48)

5d – La (57), Hf (72) to Hg (80)

6d – Ac(89), Rf(104) …………. Unb (ununbium) 112 (incomplete)

(a) From left to right in a period

The atomic size first decreases due to the increase in effective nuclear charge and then becomes constant and then increases. 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 balances the decrease in size due to increase in nuclear charge to about 80%. 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. 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 the effective nuclear charge due to d10 structure of Cu and Zn. The atomic radii of the elements of 3d transition series are as under.

ScTiVCrMnFeCoNiCuZn

1.441.321.221.181.171.171.161.161.171.25

Inner transition elements - 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. This is called lanthanide contraction. The atomic radii in Å are as under

LaCePrNdPmSmEuGd

1.881.821.831.82 –1.802.041.80

TbDyHoErYbLu

1.781.771.761.751.941.73

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 4ƒ-orbitals respectively.

Cause of Lanthanide contraction – In lanthanides the additional electrons enters the (n-2)ƒ orbital. The mutual shielding effect of (n-2)ƒ electrons is very little because the shape of ƒ-subshell is very much diffused. Thus the effective nuclear charge increases then the mutual shielding effect of (n-2) ƒ 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 5ƒ-electrons which are therefore pulled more strongly by the nucleus.

(b) In a group

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.

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 IIIB. The difference is about 0.02Å.

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