The modem periodic law states that, "the physical and chemical properties of the elements are periodic functions of their atomic numbers."

It is defined as the relative tendency of an element present in a covalently bonded molecule, to attract the shared pair of electrons towards itself.

Ions of different elements having the same number of electrons are called isoelectronic ions.

Ions of different elements	Na+	Mg+2	Al+3	F-	O2-	N3-
No. of electrons	10	10	10	10	10	10

(i) Due to low bond dissociation enthalpy, high electronegativity and large negative electron gain enthalpy, halogen have a strong tendency to accept electrons and thus get reduced.
X²+2e^- ⟶ 2X^-
(ii) The ready acceptance of an electron is due to the strong oxidising nature of halogens.
(iii) F₂ is the strongest oxidising halogen and it oxidises other halide ions in solution or even in the solid phase. In general, a halogen oxidises halide ions of higher atomic number.
(iv) Hence, the oxidising ability of halogens decreases from fluorine to iodine as :
F₂ > Cl₂ > Br₂ > I₂

(i) According to aufbau's principle 5th period has nine orbital (one 5s, five 4d and three 6p) to be filled.
(ii) Nine orbitals can accommodate a maximum of 18 electrons. Hence fifth period of the periodic table should has 18 elements from rubidium (2 = 37) to Xenon (Z = 54).

Ionisation energy is the amount of energy required to remove the electron from the ground state (EI) to excited state (E^∞)
E₁=-2.18 x 10^-18 J; E_∞=0
ΔE=E_∞-E₁
=0-(-2.18 x 10^-18 J)=2.18 x 10^-18 J
I.E per hydrogen atom = 2.18 x 10^-18 J
I.E per mole of H-atom =2.18 x 10^-18 J x 6.023 x 10²³
=13.13 x 10⁵ J mol^-1

The electronic configuration of Sodium (Z = 11) Is²2s²2p⁶3s¹.
Magnesium (Z = 12) 1s²2s²2p⁶3s²
Magnesium atom has a smaller radius and higher nuclear charge than a sodium atom, thus more energy will be required to remove the electron from the same orbital (3s), making the first ionisation energy of magnesium higher than that of sodium.
However, the second ionization enthalpy of sodium is higher than that of magnesium. This is because after losing 1 electron, sodium attains the stable noble gas configuration of neon (1s²2s²2p⁶). On the other hand, magnesium, after losing 1 electron still has one electron in the 3s-orbital(1s²2s²2p⁶3s¹). In order to attain the stable noble gas configuration, Thus, the energy required to remove the second electron in case of sodium is much higher than that required in case of magnesium. Hence, the second ionization enthalpy of sodium is higher than that of magnesium.

(i) Ionic radius of uni-univalent crystal can be calculated using Pauling's method from the inter ionic distance between the nuclei of the cation and anion.
(ii) Pauling assumed that ions present in a crystal lattice are perfect spheres, and they are in contact with each other therefore,
d=rC⁺ + r_A^-   ...(1)
Where d is the distance between the centre of the nucleus of cation C+ and anion A-and rC⁺, rA^- are the radius of the cation and anion respectively.
(iii) Pauling also assumed that the radius of the ion having noble gas electronic configuration is inversely proportional to. the effective nuclear charge.
\({ r }_{ C }^{ + }\alpha \frac { 1 }{ ({ Z }_{ eff }){ C }^{ + } } \) ....(2) and
\({ r }_{ A }^{ - }\alpha \frac { 1 }{ ({ Z }_{ eff }){ A }^{ - } } \)...(3)
Where Z_eff is the effective nuclear charge and Z_eff= Z - S
Dividing the equation 1 by 3
\(\frac { { r }_{ C }^{ + } }{ { r }_{ A }^{ - } } =\frac { ({ Z }_{ eff }){ A }^{ - } }{ ({ Z }_{ eff }){ C }^{ + } } \) ...(4)
On solving equation and (1) and (4) the values of r_C+ and r_A^- can be obtained.