When the elements are arranged in the order of increasing atomic numbers there is a recurrence of similar properties after certain regular intervals. This regularity is called the periodicity in properties. The distribution of electrons in the various shells determines their physical and chemical character. It has been observed that the properties of the elements depend more on the arrangements of the electrons in the outermost shell (valence shell) and not on the inner shells. This repetition of similar electronic configuration in the outermost or valence shell after certain regular intervals causes periodicity in the properties of elements.

The size of the atom is significant in governing its property. If the atom is assumed to be spherical, then the radius of the sphere gives the atomic radius. But it is difficult to exactly determine the radius of the atom because

• The probability of finding the electron is never zero even at large distances from the nucleus and so the atom does not have a well defined boundary.
• It is not possible to isolate an atom and measure its radius.
• The size of the atom changes in going from one set of environment to another and from one bonded state to another.

So, one can arbitrarily define atomic radius as the effective size which is the distance of closest approach of one atom to another atom in a given bonding situation. This approximate radius can be determined by measuring the inter-nuclear distance between the two centres of the neighbouring atoms in a covalent molecule. This is usually done by diffraction and spectroscopic techniques.

Fig: 4.3 - Calculation of atomic radius

The inter-nuclear distance corresponds to the diameter of the atom and therefore half of this distance gives the atomic radius for a homonuclear molecule like Cl-Cl or Br-Br.

Hence, it may be defined as one half of the distance between the centers of the nuclei of two similar atoms bonded by a single covalent bond. This is also called as covalent radius.

For a hetero-nuclear molecule, the covalent radius is the distance between the center of the nucleus of the atom and the mean position of the shared paired of electrons between the bonded atoms.

The covalent radii are smaller than the atomic radii in the uncombined atoms because the overlap region between atomic orbitals of two atoms becomes common in a covalent bond.

The forces of attraction (Van der Waals forces) existing between non-bonded atoms and molecules are weak and the atoms are held at larger inter-nuclear distances. Thus these radii known as Van der Waals radii are always larger than covalent radii.

Van der Waals radius is defined as one half of the inter-nuclear distance between two adjacent atoms belonging to the two nearest neighbouring molecules of the substance in the solid state.

### Variation in a period

Atomic radii in general, decrease with increase in atomic number, going from left to right in a period. This is explained on the basis of increasing nuclear charge along a period. The nuclear charge increases progressively by one unit while the corresponding addition of one electron takes place in the same principal shell. As the electrons in the same shell do not screen each other from the nucleus, the nuclear charge is not neutralized by the extra valence electron. Consequently the electrons are pulled closer to the nucleus by the increased effective nuclear charge resulting in the decrease in the size of the atom. In this way the atomic size goes on decreasing across the period.

Fig: 4.4 - Variation of atomic radius with atomic number in a period

The atomic radius abruptly increases in the case of noble gas element Neon as it does not form covalent bonds. So the value of Neon radius is Van der Waals radius which is considerably higher than the value of other covalent radii.

### Variation in a group

The atomic radii of elements increases from top to bottom in a group because the nuclear charge increases with increasing atomic number. Although, there is an increase in the principal quantum number from one atom to another, the number of electrons in the valence shell remain the same. The effect of increase in the size of the electron cloud out weighs the effect of increased nuclear charge and so the distance of the valence electron from the nucleus increases down the group. Thus the size of the atom goes on increasing down the group in spite of increasing nuclear charge.

Fig: 4.5 - Variation of atomic radius with atomic number in a group

### Problem

4.The atomic mass of germanium is 72.6 and its density is 5.47g cm-3. What is the atomic volume of germanium?