Methane (CH₃) shows the sp³ hybridisation .So , the geometry of methane molecule is tetrahedral .

Heisenberg's uncertainty principle : It is notpossible to determine precisely both theposition and the momentum (or velocity) of asmall moving particle (e.g , electron , proton etc)

$∆$x .$∆$p$⩾$$\frac{\mathrm{h}}{4\mathrm{\pi }}$

where $∆$x , $∆$p are the uncertainties with regardto position , momentum respectively .

E = mc²

E = hv

mc²= hv

$\mathrm{\nu }$=$\frac{{\mathrm{mc}}^2}{\mathrm{h}}$=$\frac{1.1\times {10}^{-23}\times 3\times {10}^8}{6.6\times {10}^{-34}}$

= 5 x 10¹⁸ Hz

Heat of neutralisation for strong acid and strongbase is always close to 13.7 kcal .

$\underset{\mathrm{strong}\mathrm{acid}}{\mathrm{HA}}$+$\underset{\mathrm{strong}\mathrm{base}}{\mathrm{BOH}}$$\rightleftharpoons$H₂O + AB

$∆$H = - 13.7 Kcal

The heat of neutralisation of strong acid andstrong base is actually the heat of formation of1 gmole of water from 1 g of H⁺ and 1 g of OH^- .

0.02 M HCl = 2 x 10^-2 M HCl

[H⁺] = 2 x 10^-2

pH = - log[H⁺]

= - log [2 x 10^-2]

= - log 2 + 2 log 10

= - 0.3010 + 2

= 1.7

Mg(OH)₂$\rightleftharpoons$Mg²⁺ + 2OH^-

K_sp = [Mg²⁺][OH^-]²

1.4 X 10^-11 = (s)(2s)²

1.4 X 10^-11 = 4s³

s = 1.5 x 10^-4 mol/L

($\because$Mol. wt. of Mg(OH)₂ = 52)

=58 X 1.5 x 10^-4

= 0.0087 g/L

Hess's law is based upon conservation of energy .

Bond energy :It may be defined as the energyreleased when two atoms get bonded or it isequal to the energy required to break the bondto form the neutral atoms .

e.g , H-H (g)$\to$H + H ,$∆$H = + 103 Kcal/mol

$\because$Heat evolved during the formation of 44 g ofCO₂= - 93kJ

$\therefore$Heat evolved in the formation of 0.156 kgof CO₂

=$\frac{-393\times 156}{44}$

= - 1393 kJ

Orbital angular momentum =$\sqrt{\mathrm{l}(\mathrm{l}+1)}$$\frac{\mathrm{h}}{2\mathrm{\pi }}$

where l = azimuthal quantum number

$\frac{\sqrt{6}\mathrm{h}}{2\mathrm{\pi }}$