Radius of the nucleus = \(1.33\times { 10 }^{ -11 }\times A^{ 1/3 }m\)
Density of nucleus \(=\frac { mass }{ volume } \)
\(=\frac { A\times 1.66\times 10^{ -27 }kg }{ \frac { 4 }{ 3 } \times \pi \times (1.33\times 10^{ -11 }\times { A }^{ 1/3 })^{ 3 } } \)
 = constant
Thus, density of nucleus is constant, independent of the element under consideration.

Bond order is defined as one half the difference between the number of electron present in the bonding and anti-bonding orbitals, i.e
Bond order (BO) \(=\frac { 1 }{ 2 } ({ N }_{ b }-{ N }_{ a })\)
A positive bond order means a stable molecule while a negative or zero bond order means an unstable molecule.
Stability of a molecule \(\propto \) bond order
Bond length \(\propto \) \(\frac { 1 }{ bond \ order } \)
Bond order values 1,2 or 3 corresponding to single, double or triple bonds respectively.

\({ NH }_{ 4 }^{ + }\) ion contains covalent and dative bonds. (It is formed by donation of lone pair of electrons on N in NH₃ to H⁺ ion). \({ NO }_{ 3 }^{ - }\) ion also contains covalent and davite bonds.
Bond between \({ NH }_{ 4 }^{ + }\) and \({ NO }_{ 3 }^{ - }\) ions is ionis.
N of \({ NH }_{ 4 }^{ + }\) ion is sp³ hydridised and is tetrahedral.
N of \({ NO }_{ 3 }^{ - }\) ion is sp² hybridised and is planar.

Energy taken by a man = 10000 kJ
Change in internal energy per day = 12500 - 10000 = 2500 kJ
The energy is lost by the man as he expends more energy than he takes.Now 100g of sugar corresponds to energy = 1632 kJ loss in energy.
2000g of sugar corresponds to energy = \(\frac { 1632\times 2000 }{ 100 } \)
= 32640 kJ
Number of days required to lose 2000g of weight or 32640 kJ of energy = \(\frac { 32640 }{ 2500 } \) = 13days

\({ CaSO }_{ 4 }\rightleftharpoons { Ca }^{ 2+ }+{ SO }_{ 4 }^{ 2- };{ K }_{ sp }=9.1\times { 10 }^{ -6 }\)
     S             S             S
Where s is the solubility of CaSO₄
\({ K }_{ sp }=\left[ { Ca }^{ 2+ } \right] \left[ { SO }_{ 4 }^{ 2- } \right] =S.S={ S }^{ 2 }\)
\(S=\sqrt { { K }_{ sp } } =\sqrt { 9.1\times { 10 }^{ -6 } } \Rightarrow S=3.017\times { 10 }^{ -3 }M\)
Solubility of CaSO₄ = 3.017 x 10^-3 mol^-1
= 3.017 x 10^-3 x 136 gL^-1
(Molar mass of CaSO₄ =136 g mol^-1)
= 410.3 x 10^-3 gL^-1
410.3x10^-3 g CaSO₄ is dissolved in = 1L
1g CaSO₄ is dissolved in = \(\frac { 1\times 1 }{ 410.3\times { 10 }^{ -3 } } \) = 2.437 L

Due to this property hydrogen is used in atomic hydrogen welding/cutting torch.

Due to this property dihydrogen is used for the manufacture of ammonia (Haber's process)
\(N_{ 2 }(g)+3H_{ 2 }(g)\overset { 673K, \ 200 \ atm }{ \underset { Fe,Mo }{ \rightleftharpoons } } 2NH_{ 3 }(g)\)

Producer gas is a mixture of CO and N₂, therefore, the tetravalent element is carbon and its monoxide and dioxide are CO and CO₂ respectively.
\(2C(s)+\underbrace { O_{ 2 }(s)+4N_{ 2 }(g) }_{ Air } \overset { 1273k }{ \rightarrow } \underbrace { 2CO(g)+4N_{ 2 }(g) }_{ Producer \ gas } \)
The carbon monoxide is a strong reducing agent and reduces ferric oxide to iron.
\(Fe_{ 2 }O_{ 3 }(s)+3CO(g)\overset { \Delta }{ \rightarrow } 2Fe(s)+3CO_{ 2 }(g)\)

The general formula of alkanes is C_nH_2n+2=12xn+1x(2n+2)=72 or 12n+2n+2=72 or n=5
Thus, the molecular formula of the alkane is C₅H₁₂. For structural isomers and their IUPAC names.