Periodic trends in physical properties
Atomic Radii
Atomic radii can be defined as the distance of the outermost shell of an atom from the centre of its nucleus. Being very small, it is usually expressed in nm (1 nm = 10 Ao = 103 pm = 10-9 m). The size of an atom is considered to be approximately 1.2 Ao or 0.12 nm.
Though the definition seems to be very simple considering the atom as a spherical object with well-defined boundaries. But quantum mechanics gives a contradictory theory neglecting a sharp boundary. Based on the probability concept, an atom does not have a well-defined boundary. Since probability of finding an electron is never zero even at large distances from the nucleus, the exact value of atomic radius cannot be calculated. So, atomic radius is taken as the effective size which is the distance of closest approach of one atom to the another atom in a given bonded situation.
Various names had been proposed for the atomic radii depending upon their experimental determinations and nature of atom. These are :
(i) Covalent radius (ii) Metallic radius
(iii) Ionic radius (iv) van der Waals radius
(i) Covalent radius:
Covalent bond is normally formed between the non-metals hence this term, covalent radius is used for them. It is defined as half of the internuclear distance between two successively covalently bonded atoms in a molecule. We can measure atomic radii by X-ray or other spectroscopic methods.
Covalent radius = 1\2 *distance between the nuclei of two bonded atoms
Covalent radius can be of either homodiatomic molecule like that of H2, Cl2, Br2 etc. or heterodiatomic molecules like that of HCl, HBr, etc.
If we observe the trend in atomic radii across the period and down the group , we find that the atomic size generally decreases across the period whereas there is an increase in the size down the group. The reason which can be attributed to this variation is the nuclear charge.
In a period as the atomic number increases, the increasing number of electrons are added to the same valence shell. This increases the effective nuclear charge, consequently the force of attraction of the electrons to the nucleus goes on increasing. The gradual increase in the effective nuclear charge results in the decreases of the atomic size. Down the group or in the vertical column of the periodic table there is a regular increase in the principal quantum number (n) due to the addition of a new shell.
The added new shell increases the distance of the valence electrons from the nucleus, consequently the size of the atom increases. So even though the atomic number goes on increasing, the size increases because an another factor known as ‘shielding effect’ comes into play. The lower energy level electrons (inner energy levels) are filled with electrons which serve to shield the outer electrons from the pull of the nucleus, hence, the magnitude of the nuclear attraction decreases.
(ii) Metallic radius:
Metallic radius is taken as half of the distance between two successive nuclei of two adjacent metal atoms.
Factors which affect the atomic radii
1. No. of the shells – Larger the no. of the shells filled with electrons, larger will be the size.
2. Nuclear charge – Nuclear charge (+ve) attract the electrons towards nucleus and tries to decreases the size.
Generally, along the period, size decreases because atomic number increases across the period and hence, nuclear charge increases as electrons are filled in the same shell.
Along the group size generally increases, however nuclear charge also increases that tries to minimize the size but at every step new shell is required to fill the electron and hence size increase down the group.
3. Screening effect or Shielding effect – The inner layer of the electrons act as a shield between nucleus and the outermost electron. The effect is known as shielding effect.
Screening power of different subshells is in the order s > p > d > f , and shielding effect tires to increase the size.
Note: Metallic radius or crystal radius depends on co-ordination number.
(iii) Ionic radius:
The removal of an electron from an atom results in the formation of a cation, whereas the gain of electron leads to the formation of an anion. The strong electrostatic force of attraction between the positively charged cation and the negatively charged anion causes them to come closer forming a crystal lattice (arrangement of ions in a definite and repeated manner). The ionic radii can be estimated be measuring the distances between cations and anions in the ionic crystal.
So, the ionic radius can be defined as the distance of outermost shell of an anion or cation from its nucleus.
For example: the bond length (dA-B) between an ionic molecule is given as
dA-B = rc + ra
In general, the ionic radii of elements exhibit the same trend as atomic radii. The size of a cation is always smaller than its parent atom because the cation formed after the loss of electron has fewer electrons. Though the nuclear charge remains the same, effective nuclear charge increases. So the remaining electrons are more strongly pulled towards nucleus, thus reducing the size of the cation.
For example: the atomic radius of sodium is 186 pm whereas the ionic radius for sodium ion (Na+) is 95 pm.
The size of the anion is always larger than the parent atom because the anion formed by the gain of electron has more electrons. The addition of one or more electrons results in the increased repulsion among the electrons and a decreased effective nuclear charge. This decrease in the effective nuclear charge causes for loosening of force of nuclear attraction resulting in the increase of the size of the anion. For example, the ionic radius of fluorine is 136 pm whereas the atomic radius is 64 pm.
Isoelectronic species:
There are atoms and ions which contain the same number of electrons. These are known as isoelectronic species.
For example, The radii of these isoelectronic spieces would be different because of their different nuclear charges. As already explained the size of the cation is always smaller than the parent atom whereas the size of the anion is always larger than its parent. The successive loss of electrons from an atom increases the effective nuclear charge whereas the successive gain of electrons decreases the effective nuclear charge. This is the reason the cation with a greater positive charge has a smaller radius because of the greater nuclear attraction of the electrons. While the anion with the greater negative charge has a larger radius because in this case the net repulsion of the electrons outweigh the nuclear charge and causes for the expansion in size.
(iv) van der Waals radius:
It is defined as half the distance between the nuclei of two non-bonded neighboring atoms of two adjacent molecules in solid state. This term is used for non-metals (in covalent compounds) and noble gases. For example, the van der Waals radius of chlorine is 180 pm.
van der Waals radius =1\2 x d (Internuclear distance between two non-bonded neighbouring atoms of two covalently bonded molecules)
van der Waal’s radius of chlorine = 1\2 x 360 = 180 pm
In case of noble gases we can only measure van der Waals radius because they normally do not form chemical compounds and are held together by weak forces of attraction at large internuclear distances. This is the reason, van der Waals radius is always larger than the covalent radius. The same reason can be attributed to the noble gases having the largest radii in their respective periods.