WORLD CRYPTO AND NET

☑️Revision Notes on Biodiversity and Conservation (1) The vast array of species of micro-organisms, algae, fungi, plants and animals occurring on the earth either in the terrestrial or aquatic habitats and the ecological complexes of which they are a part. (2) Diversity ranges from macromolecules to biomes. (3) Biodiversity on earth exists in three levels of organization: (i) Genetic diversity (ii) Species diversity (4) Genetic diversity (i) It is related to the variations of genes within species. (ii) The variations may be in different variants of same genes (alleles), in entire genes or in chromosomal structures. (ii) Greater the genetic diversity among organisms of a species, more sustenance it has against environmental perturbations. (iii) Genetically uniform populations are highly prone to diseases. (5) Species diversity (i) it is related to the variety of species within a region. (ii) Species richness refers to the number of species per unit area. (iii) Species Evenness refers to the relative abundance with which each species is represented in an area. Biodiversity in India (1) Out of the twelve mega biodiversity counties, India is one. (2) India has 10 biogeographical regions, 89 national parks, 500 wild life sanctuaries, 14 biosphere reserves, 6 westlands and 35 world heritage sites. (3) There are about 45,000 species of plants and about 90,000-1,00,000 species of animals. Patterns of Biodiversity (1) Biodiversity changes with change in latitude or altitude. (2) It is minimum at the poles and maximum near or at equator. Similarly, as one moves down from higher to lower altitudes, biodiversity is increased. Loss of bio-diversity: (1) Caused by three factors - Population, Urbanisation and Industrialisation. (2) The colonisation of tropical Pacific Islands by human has led to the extinction of more than 2000 species of native birds. (3) Loss of bio-diversity in a region leads to: (i) decrease in plant production. (ii) less resistance to environmental disturbances such as droughts. (iii) increase in variability in ecosystem processes like plant productivity, water use, pest and disease cycles etc. Biodiversity Conservation In situ conservation (1) The most appropriate method to maintain species of wild animals and plants in their natural habitats. This approach includes conservation and protection of the total ecosystems and its biodiversity through a network of protected areas. (2) The common natural habitats (protected areas) that have been set for in-situ conservation of wild animals and plants include: (i) National parks (ii) Wild life sanctuaries (iii) Biosphere reserves (iv) Several wetlands, mangroves and coral reefs. (v) Sacred grooves and lakes. (3) Hot spot of biodiversity are those regions of rich biodiversity which have been declared sensitive due to direct or indirect interference of human activities. (4) There are 25 terrestrial hot spots in the world including two from India. Ex situ conservation (1) Threatened animals and plants are taken out from their natural habitat and placed in special setting where they can be protected and given special care. (2) Ex situ conservation includes the following: (i) Sacred plants and home gardens (ii) Seed banks, field gene banks, cryopreservation. (iii) Botanical gardens, Arborata, Zoological gardens, Aquaria. Convention on Biodiversity: (1) “The earth Summit” held in Rio de Jeneiro in 1992 called upon all nations to take appropriate measures for conservation of biodiversity and sustainable utilization of its benefits. (2) Second international Conference on Sustainable development held in 2002 in Johannesburg, South Africa, 190 countries pledged their commitment to achieve by 2010 a significant reduction in the current rate of biodiversity loss at global, regional and local level. ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

✅Notes on s-Block Elements: Covalent Character:. Small cation and large anion favors covalency. Order: LiCl > NaCl > KCl > RbCl > CsCl & . LiI > LiBr > LiCl > LiF Greater the charge on the cation greater is its polarizing power and hence larger is the covalent character: Na+CI- < Mg+2CI2 < AI+3 CI3 Greater the charge on the anion, more easily it gets polarized thereby imparting more covalent character to the compound formed eg covalent character increase in the order. NaCI < Na2SO4 < Na3PO4 c) Lattice Energies: Amount of energy required to separate one mole of solid ionic compound into its gaseous ions. Greater the lattice energy, higher is the melting point of the alkali metals halide and lower is its solubility in water d) Hydration Energy: Amount of energy released when one mole of gaseous ions combine with water to form hydrated ions. M+ (g) + aq → M+ (aq) + hydration energy X- (g) + aq → X- (aq) + hydration energy Higher the hydration energy of the ions greater is the solubility of the compound in water. The solubility of the most of alkali metal halides except those of fluorides decreases on descending the group since the decrease in hydration energy is more than the corresponding decrease in the lattice energy. Due to high hydration energy of Li+ ion, Lithium halides are soluble in water except LiF which is sparingly soluble due to its high lattice energy. For the same alkali metal the melting point decreases in the order fluoride > chloride > bromide > iodide For the same halide ion, the melting point of lithium halides are lower than those of the corresponding sodium halides and thereafter they decrease as we move down the group from Na to Cs. The low melting point of LiCl (887 K) as compared to NaCl is probably because LiCl is covalent in nature and NaCl is ionic. Anomalous Behavior of Lithium and diagonal relationship with Magnesium: Li has anomalous properties due to Very small size High polarizing Power Lithium show diagonal relationship with magnesium because both elements have almost same polarizing power. The melting point and boiling point of lithium are comparatively high. Lithium is much harder than the other alkali metals. Magnesium is also hard metal. Lithium reacts with oxygen least readily to form normal oxide whereas other alkali metals form peroxides and superoxides. LiOH like Mg (OH)2 is weak base. Hydroxides of other alkali metals are strong bases. Due to their appreciable covalent nature, the halides and alkyls of lithum and magnesium are soluble in organic solvents. Unlike elements of group 1 but like magnesium. Lithium forms nitride with nitrogen.6Li + N2 → 2Li3N LiCl is deliquescent and crystallizes as a hydrate, LiCI2H2O. Other alkali metals do not form hydrates. also forms hydrate, MgCI2.8H2O . Unlike other alkali metals lithium reacts directly with carbon to form an ionic carbide. Magnesium also forms a similar carbide. The carbonates, hydroxides and nitrates of lithium as well as magnesium decompose on heating. Li2CO3 → Li2O + CO2 MgCO3 → MgO + CO2 2LiOH → Li2O + H2O Mg (OH)2 → MgO + H2O 4LiNO3 → 2Li2O + 4NO2 + O2 2Mg ( NO3)2 → 2Mg + 4NO2 +O2 The corresponding salts of other alkali metals are stable towards heat. Lithium nitrate, on heating, decomposes to give lithium oxide, Li2O whereas other alkali metals nitrate decomposes to give the corresponding nitrite. 4LiNO3 → 2Li2O + 4NO2 + O2 2NaNO3 → 2NaNO2 + O2 2KNO3 → 2KNO2 + O2 Li2CO3, LiOH, LiF and Li3PO4 are the only alkali metal salts which are insoluble in water. The corresponding magnesium compounds are also insoluble in water. Hydrogen carbonates of both lithium and magnesium can not be isolated in solid state. Hydrogen carbonates of other alkali metals can be isolated in solid state. Sodium Hydroxide (NaOH): a. Properties NaOH is stable towards heat but is reduced to metal when heated with carbon 2NaOH + 2C → 2Na +2CO + H2 FeCl3 + 3NaOH →Fe(OH)3 + 3NaCl NH4Cl + NaOH → NaCl + NH3 (pungent smell) + H2O

💠Properties of Solids and Liquids - Revision Notes on Liquids at Rest:💠 ⛔️Force of cohesion:- It is force between two molecules of similar nature. ⛔️Force of adhesion:- It is the force between two molecules of different nature. ⛔️Molecular range:- The maximum distance between two molecules so that the force of attraction between them remains effective is called molecular range. ⛔️Sphere of influence:- Sphere of influence of any molecule is the sphere with molecule as its center and having a radius equal to molecular range (=10-7 cm). ⛔️Surface film:- Surface film of a liquid is defined as the portion of liquid lying on the surface and caught between two parallel planes situated molecular range apart. ⛔️Surface Tension Surface tension is the property of a liquid by virtue of which its free surface behaves like a stretched membrane and supports, comparatively heavier objects placed over it. It is measured in terms of force of surface tension. ⛔️Force of surface tension:- It is defined as the amount of force acting per unit length on either side of an imaginary line drawn over the liquid surface. (a) T = Force/length = F/l (b) T = Surface energy/Surface area = W/A Units:- S.I – Nm-1 C.G.S- dyn cm-1 ⛔️Additional force:- (a) For a cylindrical rod:- F = T×2πr (Here r is the radius of cylindrical rod) (b) For a rectangular block:- F = T×2(l+d) (Here l is the length and d is the thickness of the rectangular block) (c) For a ring:- F = T×2×2πr (Here r is the radius of cylindrical rod) ⛔️Surface energy:- Potential energy per unit area of the surface is called surface energy. (a) Expansion under isothermal condition:- To do work against forces of surface tension:- W= T×A (Here A is the total increase in surface area) To supply energy for maintaining the temperature of the film:- E = T+H (b) Expansion under adiabatic conditions:- E = T Force of surface tension is numerically equal to the surface energy under adiabatic conditions. ⛔️Drops and Bubbles:- (a) Drop:- Area of surface film of a spherical drop of radius R is given by, A = 4πR2 (b) Bubble:- The surface area of the surface films of a bubble of radius R is, A = 2×4πR2 ⛔️Combination of n drops into one big drop:- (a) R = n1/3r (b) Ei = n (4πr2T), Ef =4πR2T (c) Ef/ Ei = n -1/3 (d) ΔE/Ei = [1-(1/n1/3)] (e) ΔE = 4πR2T (n1/3-1) = 4πR3T (1/r – 1/R) ⛔️Angle of contact:- Angle of contact, for a pair of solid and liquid, is defined as the angle between tangent to the liquid surface drawn at the point of contact and the solid surface inside the liquid. (a) When θ < 90º (acute):- Fa >Fc/√2 (i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid. (ii) Liquid molecules will stick with the solid, thus making solid wet. (iii) Such liquid is put in the solid tube; it will have meniscus concave upwards. (b) When θ > 90º (obtuse):-Fa<Fc/√2 (i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid. (ii) In this case, liquids do not wet the solids. (iii) Such liquids when put in the solid tube will have a meniscus convex upwards. (c) When θ = 90º:-? Fa=Fc/√2 The surface of liquid at the point of contact is plane. In this case force of cohesion and adhesion are comparable to each other. (d) cosθc = Tsa – Tsl/Tla Here, Tsa,Tsl and Tla represent solid-air, solid-liquid and liquid-air surface tension respectively). Here θc is acute if Tsl < Tsa while θc is obtuse if Tsl >Tsa. ⛔️Capillarity:- ?Rise of Liquid in a Capillary Tube?Capillarity is the phenomenon, by virtue of which the level of liquid in a capillary tube is different from that outside it, is called capillarity. Weight of liquid, W = Vρg = πr2[h+(r/3)]ρg (Here r is the radius meniscus) If weight of meniscus is taken into account, the force of surface tension will be, T = [r(h+(r/3)) ρg]/2 cosθ For fine capillary, force of surface tension, T = rhρg/2 cosθ So height, h = 2T cosθ/ rρg

✅Notes on s-Block Elements: Physical Properties of Alkali Metals: ➖These are soft in nature and can be cut with the help of knife except the lithium. ➖The atoms of alkali metals have the largest size in their respective periods. ➖The first ionization energy of the alkali metals are the lowest as compared to the elements in the other group. ➖The alkali metals show +1 oxidation state. ➖The alkali metals have low values of reduction potential (as shown in table-I) and therefore have a strong tendency to lose electrons and act as good reducing agents. ➖The melting and boiling points of alkali metals are very low because the intermetallic bonds in them are quite weak. Hydroxides of Alkali Metals: a)All the alkali metals, their oxides, peroxides and superoxides readily dissolve in water to produce corresponding hydroxides which are strong alkalies. ➖2Na + 2H2O → 2NaOH + H2 ➖Na2O + 2H2O 2NaOH ➖Na2O2 + 2H2O → 2NaOH + H2O2 ➖2KO2 + 2H2O → 2KOH + H2O2 + O2 b) The basic strength of these hydroxides increases as we move down the group Li to Cs. c) All these hydroxides are highly soluble in water and thermally stable except lithium hydroxide. d) Alkali metals hydroxides being strongly basic react with all acids forming salts. ➖NaOH + HCI → NacI + H2O ➖2NaOH + H2 SO4 → Na2SO4 + 2H2O Halides of Alkali metals: ➖M2O + 2HX → 2MX + H2O ➖MOH + HX → MX + H2O ➖M2CO3 + 2HX → 2MX + CO2 + H2O (M = Li, Na, K, Rb or Cs) (X = F, Cl, Br or I) ➖ll the alkali metals form ionic (electrovalent) compounds. ➖The alkali metals are good conductors of heat and electricity. ➖Alkali metals (except Li) exhibit photoelectric effect ➖The alkali metals and their salts impart a characteristic colour to flame.

✅Notes on s-Block Elements: Physical Properties of Alkali Metals: ➖These are soft in nature and can be cut with the help of knife except the lithium. ➖The atoms of alkali metals have the largest size in their respective periods. ➖The first ionization energy of the alkali metals are the lowest as compared to the elements in the other group. ➖The alkali metals show +1 oxidation state. ➖The alkali metals have low values of reduction potential (as shown in table-I) and therefore have a strong tendency to lose electrons and act as good reducing agents. ➖The melting and boiling points of alkali metals are very low because the intermetallic bonds in them are quite weak. Hydroxides of Alkali Metals: a)All the alkali metals, their oxides, peroxides and superoxides readily dissolve in water to produce corresponding hydroxides which are strong alkalies. ➖2Na + 2H2O → 2NaOH + H2 ➖Na2O + 2H2O 2NaOH ➖Na2O2 + 2H2O → 2NaOH + H2O2 ➖2KO2 + 2H2O → 2KOH + H2O2 + O2 b) The basic strength of these hydroxides increases as we move down the group Li to Cs. c) All these hydroxides are highly soluble in water and thermally stable except lithium hydroxide. d) Alkali metals hydroxides being strongly basic react with all acids forming salts. ➖NaOH + HCI → NacI + H2O ➖2NaOH + H2 SO4 → Na2SO4 + 2H2O Halides of Alkali metals: ➖M2O + 2HX → 2MX + H2O ➖MOH + HX → MX + H2O ➖M2CO3 + 2HX → 2MX + CO2 + H2O (M = Li, Na, K, Rb or Cs) (X = F, Cl, Br or I) ➖ll the alkali metals form ionic (electrovalent) compounds. ➖The alkali metals are good conductors of heat and electricity. ➖Alkali metals (except Li) exhibit photoelectric effect ➖The alkali metals and their salts impart a characteristic colour to flame.

✍️Notes on Biotechnology Steps of recombinant DNA technology (1) Isolating a useful DNA segment from the donor organism. (2) Splicing it into a suitable vector under conditions to ensure that each vector receives no more than one DNA fragment. (3) Producing of multiple copies of his recombinant DNA. (4) Inserting this altered DNA into a recipient organism. (5) Screening of the transformed cells. Vectors: Vector in genetic engineering is usually a DNA segment used as a carrier for transferring selected DNA into living cells. These are as follows: (1) Plasmid: Plasmid is extra chromosomal, closed circular double stranded molecules of DNA present in most eukaryotes. All plasmid carry replicons pieces of DNA that have the genetic information required to replicate. Plasmid pBR 322 was one of the first widely used cloning vectors, it contain both ampicillin and tetracycline resistance genes. (2) Phage: It is constructed from the phage l chromosomes and acts as bacteriophage cloning vectors. (3) Cosmid: The hybrids between plasmid and the phage l chromosome give rise to cosmid vectors. (4) Beside all these there are artificial chromosomes like (i) BACs (Bacterial Artificial chromosomes) (ii) YACs (Yeast Artificial chromosomes) (iii) MACs (Mammalian Artificial chromosomes) are very efficient vectors for eukaryotic gene transfers. Application of recombinant DNA technology: The technique of recombinant DNA can be employed in the following ways. (1) It can be used to elucidate molecular events in the biological process such as cellular differentiation and ageing. The same can be used for making gene maps with precision. (2) In biochemical and pharmaceutical industry, by engineering genes, useful chemical compounds can be produced cheaply and efficiently which is shown in table.

♻️Important Notes - Electrochemical Cells♻️ ► An electrochemical cell can convert electrical energy to chemical energy and can also convert electrical energy to chemical energy. There are two types of electrochemical cells- Galvanic cell and Electrolytic cell. ► Cathodes are usually metal electrodes. It is the electrode where reduction takes place. The cathode is the positive electrode in a galvanic cell and a negative electrode in an electrolytic cell. Electrons move into the cathode. ► A half-cell is half of an electrochemical cell (electrolytic or galvanic), where either oxidation or reduction occurs. At equilibrium, there is no transfer of electrons across the half cells. Therefore, the potential difference between them is nil. ► A salt bridge is a device used to connect the oxidation and reduction half-cells of a galvanic cell (a type of electrochemical cell). Strong electrolytes are generally used to make the salt bridges in electrochemical cells. Since ZnSO4 is not a strong electrolyte, it is not used to make salt bridges. ► Emf of a cell is equal to the maximum potential difference across its electrodes, which occurs when no current is drawn through the cell. It can also be defined as the net voltage between the oxidation and reduction half-reactions. ► Cell potential is an intensive property as it is independent of the amount of material present. Gibbs free energy is defined for an electrochemical cell and is an extensive property as it depends on the quantity of the material. ► Electrode potential is the tendency of an electrode to accept or to lose electrons. Electrode potential depends on the nature of the electrode, temperature of the solution and the concentration of metal ions in the solution. It doesn’t depend on the size of the electrode. ► The salt bridge connects the two half-cell solutions to complete the circuit of the electrochemical cell. The electrolytes of the salt bridge are generally prepared in agar-agar or gelatin so that the electrolytes are kept in a semi-solid phase and do not mix with the half-cell solutions and interfere with the electrochemical reaction. ► A salt bridge is a junction that connects the anodic and cathodic compartments in a cell or electrolytic solution. It maintains electrical neutrality within the internal circuit, preventing the cell from rapidly running its reaction to equilibrium. ► A Voltaic or Galvanic cell is a type of electrochemical cell that converts chemical energy into electrical energy. Photovoltaic cells are used to convert light energy into electrical energy. An Electrolytic cell is a type of electrochemical cell that converts electrical energy into chemical energy. A fuel cell is an electrochemical cell that converts the chemical energy of a fuel and an oxidizing agent into electricity. ► For all spontaneous chemical reactions, the change in Gibbs free energy (ΔG°) is always negative. For a spontaneous reaction in an electrolytic cell, the cell potential (E°cell) should be positive. ► In an electrochemical cell, when an opposing externally potential is applied and increased slowly, the reaction continues to take place. When the external potential is equal to the potential of the cell, the reaction stops. Once the externally applied potential is greater than the potential of the cell, the reaction goes in the opposite direction and the cell behaves like an electrolytic cell. ► Primary cells cannot be used again and again. Since there is no fluid inside, these cells are also known as dry cells. The internal resistance is high and the chemical reaction is irreversible. Their initial cost is cheap. ► A secondary battery (a series of cells) is one which can be charged, discharged into a load, and recharged many times. Nickel-cadmium cell, Lead storage cell and Mercury cell are examples of secondary cells. Leclanche cell is an example of a primary cell.

🧩Algebra- Revision Notes on Probability🧩 ➖➖➖➖➖➖➖➖➖➖➖➖ The sum of all the probabilities in the sample space is 1. The probability of an event which cannot occur is 0. The probability of any event which is not in the sample space is zero. The probability of an event which must occur is 1. The probability of the sample space is 1. The probability of an event not occurring is one minus the probability of it occurring. The complement of an event E is denoted as E' and is written as P (E') = 1 - P (E) P (A∪B) is written as P (A + B) and P (A ∩ B) is written as P (AB). If A and B are mutually exclusive events, P(A or B) = P (A) + P (B) When two events A and B are independent i.e. when event A has no effect on the probability of event B, the conditional probability of event B given event A is simply the probability of event B, that is P(B). If events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by P (A and B) = P (A) P (B|A). A and B are independent if P (B/A) = P(B) and P(A/B) = P(A). If E1, E2, ......... En are n independent events then P (E1 ∩ E2 ∩ ... ∩ En) = P (E1) P (E2) P (E3)...P (En). Events E1, E2, E3, ......... En will be pairwise independent if P(Ai ∩ Aj) = P(Ai) P(Aj) i ≠ j. P(Hi | A) = P(A | Hi) P(Hi) / ∑i P(A | Hi) P(Hi). If A1, A2, ……An are exhaustive events and S is the sample space, then A1 U A2 U A3 U ............... U An = S If E1, E2,….., En are mutually exclusive events, then P(E1 U E2 U ...... U En) = ∑P(Ei) If the events are not mutually exclusive then P (A or B) = P (A) +P (B) – P (A and B) Three events A, B and C are said to be mutually independent if P(A∩B) = P(A).P(B), P(B∩C) = P(B).P(C), P(A∩C) = P(A).P(C), P(A∩B∩C) = P(A).P(B).P(C) The concept of mutually exclusive events is set theoretic in nature while the concept of independent events is probabilistic in nature. If two events A and B are mutually exclusive, P (A ∩ B) = 0 but P(A) P(B) ≠ 0 (In general) ⇒ P(A ∩ B) ≠ P(A) P(B) ⇒ Mutually exclusive events will not be independent. The probability distribution of a count variable X is said to be the binomial distribution with parameters n and abbreviated B (n,p) if it satisfies the following conditions: The total number of observations is fixed The observations are independent. Each outcome represents either a success or a failure. The probability of success i.e. p is same for every outcome. Some important facts related to binomial distribution: (p + q)n = C0Pn + C1Pn-1q +...... Crpn-rqr +...+ Cnqn The probability of getting at least k successes out of n trials is P(x > k) = Σnx = k nCxpxqn-x Σnx = k nCxqn-xpx = (q + p)n = 1 Mean of binomial distribution is np Variance is npq Standard deviation is given by (npq)1/2, where n Sum of binomials is also binomial i.e. if X ~ B(n, p) and Y ~ B(m, p) are independent binomial variables with the same probability p, then X + Y is again a binomial variable with distribution X + Y ~ B(n + m, p). If X ~ B(n, p) and, conditional on X, Y ~ B(X, q), then Y is a simple binomial variable with distributionY ~ B( n, pq). The Bernoulli distribution is a special case of the binomial distribution, where n = 1. Symbolically, X ~ B (1, p) has the same meaning as X ~ Bern (p). If an experiment has only two possible outcomes, then it is said to be a Bernoulli trial. The two outcomes are success and failure. Any binomial distribution, B (n, p), is the distribution of the sum of n independent Bernoulli trials Bern (p), each with the same probability p. The binomial distribution is a special case of the Poisson Binomial Distribution which is a sum of n independent non-identical Bernoulli trials Bern(pi). If X has the Poisson binomial distribution with p1 = … = pn = p then X ~ B(n, p). A cumulative binomial probability refers to the probability that the binomial random variable falls within a specified range (e.g., is greater than or equal to a stated lower limit and less than or equal to a stated upper limit).

Differential Calculus: Notes on Maxima and Minima Local Maximum: A function f(x) is said to have a local maximum at x = a if the value of f(a) is greater than all the values of f(x) in a small neighbourhood of x = a. Mathematically, f (a) > f (a – h) and f (a) > f (a + h) where h > 0, then a is called the point of local maximum. Local Minimum: A function f(x) is said to have a local minimum at x = a, if the value of the function at x = a is less than the value of the function at the neighboring points of x = a. Mathematically, f (a) < f (a – h) and f (a) < f (a + h) where h > 0, then a is called the point of local minimum. A point of local maximum or a local minimum is also called a point of local extremum. A point where the graph of function is continuous and has a tangent line and where the concavity changes is called point of inflexion. At the point of inflexion, either y” = 0 and changes sign or y” fails to exist. At the point of inflexion, the curve crosses its tangent at that point. A function cannot have point of inflexion and extrema at the same point. Working rules to find points of local maxima and local minima: 1. First Derivative Test: If f'(a) = 0 and f'(x) changes its sign while passing through the point x = a, then f(x) would have a local maximum at x = a if f'(a – 0) > 0 and f'(a + 0) < 0. It means that f'(x) should change its sign from positive to negative. f(x) would have local minimum at x = a if f'(a – 0) < 0 and f'(a + 0) > 0 . It means that f'(x) should change its sign from negative to positive. If f(x) doesn’t change its sign while passing through x = a, then f (x) would have neither a maximum nor minimum at x = a. e.g. f (x) = x3 doesn’t have any local maxima or minima at x = 0. 2. Second Derivative Test: Let f(x) be a differentiable function on a given interval and let f'' be continuous at stationary point. Find f'(x) and solve the equation f'(x) = 0 given let x = a, b, … be solutions. There can be two cases: Case (i): If f''(a) <0 then f(a) is maximum. Case (ii): If f ''(a) > 0 then f(a) is minimum. In case, f''(a) = 0 the second derivatives test fails and then one has to go back and apply the first derivative test. If f''(a) = 0 and a is neither a point of local maximum nor local minimum then a is a point of inflection. 3. nth Derivative Test for Maxima and Minima: Also termed as the generalization of the second derivative test, it states that if the n derivatives i.e. f '(a) = f''(a) = f'''(a) =………. = f n(a) = 0 and fn+1(a) ≠ 0 (all derivatives of the function up to order ‘n’ vanish and (n + 1)th order derivative does not vanish at x = a), then f (x) would have a local maximum or minimum at x = a iff n is odd natural number and that x = a would be a point of local maxima if fn+1 (a) < 0 and would be a point of local minima if fn+1 (a) > 0. In some questions involving determination of maxima and minima, it might become difficult to decide whether f(x) actually changes its sign while passing through x = a and here, nth derivative test can be applied. Global Minima & Maxima of f(x) in [a, b] is the least or the greatest value of the function f(x) in interval [a, b]. 1. The function f(x) has a global maximum at the point ‘a’ in the interval I if f (a) ≥ f(x), for all x ∈ I. 2. Function f(x) has a global minimum at the point ‘a’ if f (a) ≤ f (x), for all x ∈ I. Global Maxima Minima always occur either at the critical points of f(x) within [a, b] or at the end points of the interval. Computation of Global Maxima and minima in maxima minima problems: 1. Compute the critical points of f(x) in (a, b). Let the various critical points be C1, C2, …. , Cn. 2. Next, compute the value of the function at these critical points along with the end points of the domain. Let us denote these values by f(C1), f(C2)………..f(Cn). 3. Now, compute M* = max{f(a), f(C1), f(C2)………..f(Cn), f(b)} and M** = min{f(a), f(C1), f(C2)………..f(Cn), f(b)}.Now M* is the maximum value of f(x) in [a, b] and M** is the minimum value of f(x) in [a, b].

(a) Lactic acid: Lactic acid is commercially produced from pasteurized whey (the watery part of milk) through fermentation caused by Lactobacilus bulgaricus and L. delbrueckii. (b) Curd: Curd is prepared from pasteurized milk by the process called curdling. It is initiated by adding a starter culture of Lactobacillus bulgaricus and Streptococcus thermophillus, into the milk at 40°C. Lactobacillus converts lactose to lactic acid whereas Streptococcus causes coagulation of casein due to acidity. (c) Cheese: Preparation of cheese from the milk involves two main steps – first curdling of milk, and second the subsequent ripening of solid curd by the use of different bacterial strains. (d) Butter: It is prepared by churning of sweet or sour cream. The microorganisms responsible for preparation of butter cream are – Streptococcus lactis and Leuconostoc citrivorumare. The characteristic butter aroma develops due to a volatile substance – diacetyl. It is produced by the action of streptococcus on pasteurized milk. (e) Retting process: Fibres of flax, hemp and jute are separated by the process called retting. During this process the stems of the plants are submerged in water, where the bacterial activity results in the rotting of softer parts. The tough bast fibres become loosened and easily separated from each other. These fibres are spun and woven into various articles. (f) Vinegar: Country made vinegar is a fermentation product of cane juice, molasses or fruit juices. It is produced in two steps – first conversion of sugars into alcohols by alcholic fermentation carried by yeast, and the second, conversion of alcohol to acetic acid by the action of bacteria Acetobacter (A. orieansis, A. acetic, A. schuizenbachi, etc.). Vinegar is used in the preparation of pickles or in place of acetic acid. It is used as preservative of meats and vegetables. (v) Role of bacteria in human being: E.coli (gram-ve) bacteria live in colon region of intestine of man and other animals and play an important role in digestion process. (vi) Medicinal uses (a) Vitamins: Production of riboflavin (vitamin B2) involves the activity of bacterium – Clostridium butyticum. The well known vitamin C (ascorbic acid) is produced from sorbital by the action of Acetobactor spp. (b) Serum and vaccines: Many bacteria are used in the preparation of serums and vaccines. These substances induce immunity to various diseases in man. Serums are effective against certain diseases like diphtheria, pneumonia, etc., whereas the vaccines are effective against typhoid, smallpox, cholera, etc. (c) Enzymes: Some bacteria live in the alimentary canal of herbivorous animals like cow, horse, goat, etc. and help in the production of certain enzymes which digest the cellulose. The enzymes proteases are produced by bacteria Bacillus subtilis. Similarly, the enzyme pectinase is produced by Clostridium sp, which is used in retting of flax. (d) Antibiotics: These are the chemical substances produces by living microorganisms capable of inhibiting or destroying other microbes. These are the products of secondary and minor metabolic pathways, mostly secreted extracellularly by the microorganisms. These are used in controlling various infectious diseases. At present more than 5000 antibiotic substances are known and approximately 100 are available for medicinal use. The most important bacterium which produces maximum number of antibiotics is Streptomyces. ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

🔰 Role of Bacteria in nitrogen cycle 🔰 Nitrogen fixation: (1) Many free-living soil inhabiting bacteria such as, Azotobacter (aerobic), Clostridium (anaerobic), etc. have ability to fix atmospheric nitrogen into ammonia. (2) The other group of nitrogen fixing bacteria lives in symbiotic association with other plants. (3) The most important symbiotic nitrogen fixing bacteria is Rhizobium spp. (4) The various species of Rhizobium inhabit different leguminous plants. For example, R. leguminosarium infects soyabeans, etc. (5) They develop root nodules and fix atmospheric nitrogen into ammonia in symbiotic association with leguminous plants. (6) The fixed nitrogen is partly taken up by the leguminous plants and metabolised. (7) A part of fixed nitrogen is diffused out into the surrounding soil. Ammonification: (1) The nitrogenous compounds of the dead remains of plants, animals and their excretory products are decomposed into ammonia by a number of bacteria and other microorganisms. (2) The conversion of nitrogenous organic compounds into ammonia is termed as ammonification. (3) It is carried by many ammonifying bacteria such as Bacillus ramosus, B. vulgaris, B. mycoides, etc. Nitrification: (1) Many bacteria enhance the nitrogen fertility of soil by converting ammonium compounds to nitrites (e.g., Nitrosomonas) and nitrites into nitrates (e.g., Nitrobacter). (2) The Nitrosomonas group oxidizes ammonia into nitrite – (3)The Nitrobacter group oxidizes nitrite to nitrates – Denitrification: The nitrates and ammonia are converted to nitrous oxide and finally to nitrogen gas by several denitrifying bacteria, e.g., Pseudomonas fluorescence, P. denitrificans, Bacillus subtilis, Thiobacillus denitirficans, etc. Useful activities (i) Decay of organic wastes: Many saprotrophic bacteria act as natural scavengers by continuously removing the harmful organic wastes (i.e., dead remains of animals and plants) from man's environment. They decompose the organic matter by putrifaction and decay. The simple compounds produced as a result of decomposition and decay (viz., carbon dioxide, carbon monoxide, nitrates, sulphates, phosphates, ammonia, etc.) are either released back into the environment for recycling or absorbed by the plants as food. Thus, the bacteria play duel role by disposing of the dead bodies and wastes of organisms and by increasing the fertility of soil. (ii) Role in improving soil fertility: Saprotrophic bacteria present in soil perform various activities for their survival. Some of these activities improve the fertility of soil by formation of humus, manure, etc. (a) Humus: The microbial decomposition of organic matter and mineralization results in the formation of complex amorphous substance called humus. The humus improves the aeration, water holding capacity, solubility of soil minerals, oxidation-reduction potential and buffering capacity of the soil. (b) Composting: It is conversion of farm refuse, dung and other organic wastes into manure by the activity of saprotrophic bacteria (e.g., Bacillus stearothermophilus, Clostridium thermocellum, Thermomonospora spp, etc.) (c) Adding sulphates: A few sulphur bacteria (e.g., Beggiatoa) add sulphur into the soil by converting H2S into sulphates. (iii) Sewage, disposal: Ability of anaerobic bacteria to purify the organic matter is used in the the sewage disposal system of cities. The faeces are stored in covered reservoirs and allowed to purify. The solid matter is decomposed into liquidy sludge which is passed through coarse filters. The effluent is finally purified and drained out into the river or used as fertilizer in the fields. The common bacteria involved in sewage disposal are – Coliforms (E. coli), Streptococci, Clostridium, Micrococcus, Proteus, Pseudomonas, Lactobacillus, etc. (iv) Role in Industry: Useful activities of various bacteria are employed in the production of a number of industrial products. Some of these are given below– ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

✅ Electrolytic Cells and Electrolysis ✍️ Electrolysis is a process of passing a direct current through the electrodes to achieve a chemical reaction. It is not possible to achieve a chemical reaction when the chosen electrolyte is in a solid-state. ✍️ Aqua regia also known as royal water is a yellow-orange mixture of concentrated nitric acid and hydrochloric acid in the ratio 1:3. It is used by an alchemist to dissolve noble metals like gold and silver. ✍️ Electrodes which do not take part in the chemical reaction during electrolysis are known as inert electrodes. Gold, silver and graphite do not take part in the process, but graphite is preferred because gold and silver electrodes are expensive. ✍️ In the electrolysis of NaCl, if the electrolyte is molten NaCl, then the only ions formed after dissociation are Na+ and Cl– ions. The cathode being a negatively charged electrode attracts the positive Na+ ions and neutralizes it to form Sodium metal. ✍️ Na2SO4 dissociates into Na+ and SO42- ions in the electrolysis of aqueous Na2SO4. Na+ has much lower reduction potential than water and hence Na+ ions are not reduced at the cathode. Instead, reduction of water occurs giving out hydrogen gas at the cathode. ✍️ In the electrolysis of aqueous CuSO4, Cu2+, SO42+, H+ and OH– are the ions formed after dissociation. Copper ions have much higher reduction potential than water. Hence, these ions are easily reduced and deposited as Cu at the cathode. ✍️ Electroplating is a process that uses direct electric current to carry metal ions from anode and carry them through the electrolyte containing the metal ion to the cathode to get a coherent metal coating. ✍️ The electrolyte in electrolysis should contain the metal to be coated, gold in this case. AuCN is used because it is exceptionally stable and doesn’t resist the flow of Au+ ions from anode to cathode. ✍️ The two electrodes that are used in a Daniell cell are zinc (as anode) and copper (as cathode) electrodes which are dipped in a solution containing its own ions, generally zinc sulphate and copper sulphate. ✍️ Yes, the distance between the electrodes is directly proportional to the resistance between them. As the distance between the two electrodes increases, the resistance offered by the electrolyte increases and therefore reduces the voltage between them. ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

✅ Important Points to Remember: Electrochemistry – Galvanic Cells ✍️ A galvanic cell is a type of electrochemical cell that converts chemical energy into electrical energy. The electrochemical cell which converts electrical energy into chemical energy is called electrolytic cell. ✍️ Electrochemical cells are also called galvanic or voltaic cells, after the names of Luigi Galvani and Alessandro Volta who were the first to perform experiments on the conversion of chemical energy into electrical energy. ✍️ In a salt bridge, the electrolytes like KCl, KNO3 or NH4NO3 are preferred because their ions have almost equal transport number, viz., 0.5, i.e., they move with almost the same speed when an electric current flows through the ✍️ Galvanic cells are used to convert chemical energy into electrical energy. Two electrodes are usually set up in two separate beakers. The electrolytes taken in the two beakers are different. Galvanic cells are based upon spontaneous redox reactions. A salt bridge is used to set up this cell. ✍️ An anode is an electrode where oxidation takes place. An anode is a negative pole in a galvanic cell. In an electrolytic cell, the anode acts as the positive pole. Cathodes are electrodes where reduction takes place. ✍️ Greater the oxidation potential of metal, the more easily it can lose electrons and hence greater is its reactivity. As a result, a metal with greater oxidation potential can displace metals with lower oxidation potentials from their salt solutions. ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

♦️Revision Notes on Flow of Liquids and Viscosity♦️(2/3) ➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖ Viscosity:- Viscosity is the property of fluids by virtue of which they tend to destroy any relative motion between their layers. Velocity gradient:- Velocity gradient is defined as the rate of change of velocity with respect to distance. (a) Velocity gradient = dv/dr (b) Dimension of velocity gradient = [dv/dr] = [T-1] (c) Direction of velocity gradient is perpendicular to the direction of flow, directed in the direction of increasing velocity. (d) Average velocity gradient:- Average velocity gradient is the difference between velocities of two layers separated a unit distance apart. Average velocity gradient = Δv/Δr Newton’s law of viscosity:- In accordance to Newton’s law of viscosity, the viscous drag force depends upon the nature of fluid along with following factors:- (a) F∝A (common area of two layers) (b) F∝dv/dr (velocity gradient) (c) So, F =ηA (dv/dr) Here η is called coefficient of viscosity of fluid. Coefficient of viscosity of fluid (ηv) or fugitive elasticity:- ηv = shear stress/velocity gradient = (F/A)/(dv/dr) Modulus of rigidity(ηr):- ηr = shear stress/shear strain = (F/A)/(θ) = (F/A)/(dx/dr) Here, θ = dx/dr = displacement gradient Coefficient of viscosity (Absolute viscosity or Dynamic viscosity):- F= ηA (dv/dr) if A = 1, dv = 1, dr =1, F = η Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain (or resist) a unit relative velocity between two layers a unit distance apart. Or Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain a unit velocity gradient between its layers. Unit of η:- S.I:- η = 1 deca poise = 1 N sec/m2 Co-efficient of viscosity of a fluid is said to be one deca-poise if a tangential force of 1 N per meter square is required to maintain a relative velocity of 1 ms-1 between its layer 1 m apart. C.G.S:- η = 1 poise = 1 dyn sec/cm2 Coefficient of viscosity of a fluid is said to be one poise if a tangential force of 1 dyn per square cm is required to maintain a relative velocity of 1 cms-1 between its layers 1 cm apart. Relation between deca-poise and poise:- 1 deca-poise = 10 poise Dimension formula for η:- η = Fdr/Adv = [M1L-1T-1] Fluidity:- Reciprocal of coefficient of viscosity of a fluid is called its fluidity. Fluidity = 1/η Unit of fluidity: poise-1 Dimension of fluidity: [M-1L1T1] Kinematic viscosity:- Kinematic viscosity of a fluid is defined as the ration between its coefficient of viscosity to the density of fluid. Kinematic viscosity = η/ρ Units of kinematic viscosity:- C.G.S – 1 stoke = cm2 s-1 Kinetic viscosity of a fluid having its dynamic viscosity one poise and density one g cm-3 is said to be 1 stoke. Dimensional formula of kinematic viscosity = η/ρ = [M0L2T-1] Critical velocity (Reynold’s Number):- Critical velocity (vc) is the maximum velocity of the flow of liquid flowing in a streamlined flow. vc = NR η/ρD Here η is the coefficient of viscosity of liquid, ρ is the density of liquid and D is the diameter of the tube. Reynold’s Number, NR = ρvcD/ η Stokes law:- In accordance to Stoke’s law, force of viscosity F depend upon, (a) Co-efficient of viscosity of fluid η (b) Radius of the moving body r (c) Velocity of body v So, force of viscosity, F = 6π η r v Terminal velocity:- v = 2/9 [r2 (ρ-σ)/η] η = 2/9 [r2 (ρ-σ)g/v] Variation of viscosity with a change in temperature and pressure:- (a) Effect of temperature:- η= A /(1+Bt)c Here A, B and C are constants. Again, ηv1/2 = Aec/vt Here, A and C are constants and v is the relative velocity. (b) Effect of pressure:- Co-efficient of viscosity of liquids increases due to an increase in pressure but there is no relation, so far, to explain the effect. Change in viscosity of gases:- (a) Effect of temperature:- Co-efficient of viscosity of a gas at a given temperature is given by, η= η0AT1/2 Here T is the absolute temperature of gas.

♦️Revision Notes on Flow of Liquids and Viscosity♦️(1/3) ➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖ (Mechanical Properties of fluids):- Characteristic of Ideal fluid:- (a) It is incompressible (b) It is non-viscous (c) Flow of ideal fluid is irrational (d) It is capable of exhibiting steady flow Stream line flow:- Flow of a liquid fluid is said to be streamlined if the velocity of a molecule, at any point, coincides with that of the preceding one. Laminar and Turbulent FlowTube of flow:- A bundle of streamlines having same velocity of fluid elements, over any cross-section perpendicular to the direction of flow, is called a tube of flow. Laminar flow:- It is a special case of streamline flow in which velocities of all the molecules on one streamline is same throughout its motion. Turbulent flow:- Whenever the velocity of a fluid is very high or it rushes past an obstacle so that there is a sudden change in its direction of motion, the motion of fluid becomes irregular, forming eddies or whirlpools. This type of motion of fluid is called turbulent flow. Rate of flow (Equation of continuity):- Equation of Continuityav= Constant (a1v1=a2v2) Equation of continuity can be considered to be a statement of conservation of mass. So, v ∝ 1/a Velocity of flow of liquid varies inversely as the area of cross-section of the opening from where the liquid comes out. Total energy of a liquid:- (a) Kinetic energy:- It is the energy possessed by a liquid by virtue of its velocity. K.E = ½ mv2 K.E per unit mass = ½ v2 K.E per unit volume = ½ [mv2/V] = ½ ρv2 Here, ρ is the density of liquid. (b) Potential energy:- It is the energy possessed by a liquid by virtue of which of its position. Potential energy = mgh P.E per unit mass = mgh/m = gh P.E per unit volume = mgh/V = ρgh (c) Pressure energy:- It is the energy possessed by a liquid by virtue of its pressure. Pressure energy = p×V = m (p/ρ) Pressure energy per unit mass = p/ρ Pressure energy per unit volume = p×V /V= p Total energy:- Total energy of a liquid is the sum total of kinetic energy, potential energy and pressure energy. E= ½ mv2 +mgh+mp/ρ Total energy per unit mass = ½ v2 +gh+p/ρ Total energy per unit volume = ½ ρv2 +ρgh+p Bernoulli’s equation:- It states that the total energy of a small amount of an incompressible non-viscous liquid flowing without friction from one point to another, in a streamlined flow, remains constant throughout the displacement. (a) ½ mv2 + mgh+ mp/ρ = Constant (b) ½ v2 +gh+p/ρ = Constant (c) ½ ρv2 +ρgh+p = Constant or v2/2g + h + p/ρg = Constant The term v2/2g is called velocity head, h is called gravitational head and p/ρg is called pressure head. Therefore Bernoulli’s theorem states that in case of an incompressible, non-viscous fluid, flowing from one point to another in a streamlined flow, the sum total of velocity head, gravitational head and the pressure head is a constant quantity. Limitation of Bernoulli’s equation:- (a) Force of viscosity, which comes into play in case of fluids in motion has not been accounted for. (b) Loss of energy due to heat is not accounted for. (c) When a fluid flows in a curved path, the energy due to centripetal force is also not accounted for. If v is the relative velocity of top layer w.r.t. any other deeper layer (may be the lowest), then v is lesser for greater depth. v = K/bd or v ∝ 1/d Venturimeter:- It is a device used for measuring the rate of flow of liquids, generally water, through pipes. The rate of flow of water, Q = a1a2√2hg/[a12-a22] Torricelli’s theorem (velocity of efflux):- It states that the velocity of efflux of a liquid (V), from an orifice, is equal to the velocity acquired by a body, falling freely (v), from the surface of liquid to the orifice. So, V = v = √2gh ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

♦️Revision Notes on Arithmetic Progression♦️ If ‘a’ is the first term and ‘d’ is the common difference of the arithmetic progression, then its nth term is given by an = a+(n-1)d The sum, Sn of the first ‘n’ terms of the A.P. is given by Sn = n/2 [2a + (n-1)d] If Sn is the sum of n terms of an A.P. whose first term is ‘a’ and last term is ‘l’,Sn = (n/2)(a + l) If common difference is d, number of terms n and the last term l, then Sn = (n/2)[2l-(n -1)d] If a fixed number is added or subtracted from each term of an A.P., then the resulting sequence is also an A.P. and it has the same common difference as that of the original A.P. If each term of A.P is multiplied by some constant or divided by a non-zero fixed constant, the resulting sequence is an A.P. again. If a1, a2, a3, …, an andb1, b2, b3, …, bn, are in A.P. then a1+b1, a2+b2, a3+b3, ……, an+bn and a1–b1, a2–b2, a3–b3, ……, an–bn will also be in A.P. Suppose a1, a2, a3, ……,an are in A.P. then an, an–1, ……, a3, a2, a1 will also be in A.P. If nth term of a series is tn = An + B, then the series is in A.P. If a1, a2, a3, ……, an are in A.P., then a1 + an = a2 + an–1 = a3 + an–2 = …… and so on. In order to assume three terms in A.P. whose sum is given, they should be assumed as a-d, a, a+d. Four terms of the A.P. whose sum is given should be assumed as a-3d, a-d, a+d, a+3d Five convenient numbers in A.P. a–2b, a–b, a, a+b, a+2 b. In general, we take a – rd, a – (r – 1)d, …., a – d, a, a + rd in case we have to take (2r + 1) terms in an A.P. Likewise, any 2r terms of an A.P. should be assumed as: a – (2r-1)d, a – (2r – 3)d, …., a – d, a, a + d, ………….. , a+(2r-3)d, a + (2r-1)d. The arithmetic mean of two numbers ‘a’ and ‘b’ is (a+b)/2. The terms A1, A2, ….. , An are said to be arithmetic means between a and b if a, A1, A2, ….. , An, bis an A.P. Clearly, ‘a’ is the first term, ‘b’ is the (n+2)th term and ‘d’ is the common difference. Then, we have b = a+(n+2-1)d = a+(n+1)d Hence, this gives ‘d’ = (b-a)/(n+1) ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

🔰 Notes on Kinetic Theory of Gases 🔰 Kinetic Theory of Matter:- (a) Solids:- It is the type of matter which has got fixed shape and volume. The force of attraction between any two molecules of a solid is very large. (b) Liquids:- It is the type of matter which has got fixed volume but no fixed shape. Force of attraction between any two molecules is not that large as in case od solids. (c) Gases:- It is the type of matter does not have any fixed shape or any fixed volume. Ideal Gas:- A ideal gas is one which has a zero size of molecule and zero force of interaction between its molecules. Ideal Gas Equation:- A relation between the pressure, volume and temperature of an ideal gas is called ideal gas equation. PV/T = Constant or PV = nRT Here, n is the number of moles and R is the universal gas constant. Gas Constant:- (a) Universal gas constant (R):- R= P0 V0/T0 =8.311 J mol-1K-1 (b) Specific gas constant (r):- PV= (R/M) T = rT, Here, r = R/M Real Gas:-The gases which show deviation from the ideal gas behavior are called real gas. Vander wall’s equation of state for a real gas:- [P+(na/V)2?][V-nb] = nRT Here n is the number of moles of gas. Avogadro’s number (N):- Avogadro’s number (N), is the number of carbon atoms contained in 12 gram of carbon-12. N = 6.023×10^23 (a) To calculate the mass of an atom/molecule:- Mass of one atom = atomic weight (in gram)/N Mass of one molecule = molecular weight (in gram)/N (b) To calculate the number of atoms/molecules in a certain amount of substance:- Number of atoms in m gram = (N/atomic weight)×m Number of molecules in m gram = (N/molecular weight)×m (c) Size of an atom:- Volume of the atom, V = (4/3)πr3 Mass of the atom, m = A/N Here, A is the atomic weight and N is the Avogadro’s number. Radius, r =[3A/4πNρ]1/3\ Here ρ is the density. Gas laws:- Graph Between Pressure and Volume for Boyle's Law(a) Boyle’s law:- It states that the volume of a given amount of gas varies inversely as its pressure, provided its temperature is kept constant. PV = Constant (b) Charlers law or Gey Lussac’s law:- It states that volume of a given mass of a gas varies directly as its absolute temperature, provided its pressure is kept constant. Graph Between Volume and Temperature for Charles LawV/T= Constant V–V0/V0t = 1/273 = γp Here γp (=1/273) is called volume coefficient of gas at constant pressure. Volume coefficient of a gas, at constant pressure, is defined as the change in volume per unit volume per degree centigrade rise of temperature. (c) Gay Lussac’s law of pressure:- It states that pressure of a given mass of a gas varies directly as its absolute temperature provided the volume of the gas is kept constant. P/T = P0/T0 or P – P0/P0t = 1/273 = γp Here γp (=1/273) is called pressure coefficient of the gas at constant volume. Pressure coefficient of a gas, at constant volume, is defined as the change in pressure per unit pressure per degree centigrade rise of temperature. (d) Dalton’s law of partial pressures:- Partial pressure of a gas or of saturated vapors is the pressure which it would exert if contained alone in the entire confined given space. P= p1+p2+p3+…….. nRT/V = p1+p2+p3+…….. (e) Grahm’s law of diffusion:- Grahm’s law of diffusion states that the rate of diffusion of gases varies inversely as the square root of the density of gases. R∝1/√ρ or R1/R2 =√ρ2/ ρ1 So, a lighter gas gets diffused quickly. (f) Avogadro’s law:- It states that under similar conditions of pressure and temperature, equal volume of all gases contain equal number of molecules. For m gram of gas, PV/T = nR = (m/M) R ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

(c) Distance of closest approach, r0 = 2Ze2/(4πε0)E Here E = ½ mv2 = KE of the α particle. Bohr’s atomic model:- (a) The central part of the atom called nucleus, contains whole of positive charge and almost whole of the mass of atom. Electrons revolve round the nucleus in fixed circular orbits. (b) Electrons are capable of revolving only in certain fixed orbits, called stationary orbits or permitted orbits. In such orbits they do not radiate any energy. (c) While revolving permitted orbit an electron possesses angular momentum L (= mvr) which is an integral multiple of h/2π. L=mvr =n (h/2π) Here n is an integer and h is the Planck’s constant. (d) Electrons are capable of changing the orbits. On absorbing energy they move to a higher orbit while emission of energy takes place when electrons move to a lower orbit. If f is the frequency of radiant energy, hf= W2-W1 Here W2 is the energy of electron in lower orbit and W1 is the energy of electron in higher orbit. (e) All the laws of mechanics can be applied to electron revolving in a stable orbit while they are not applicable to an electron in transition. Bohr’s Theory of Atom:- (a) Orbital velocity of electron:- vn= 2πkZe2/nh For a particular orbit (n= constant), orbital velocity of electron varies directly as the atomic number of the substance. vn∝Z (b) For a particular element (Z= constant), orbital velocity of the electron varies inversely as the order of the orbit. vn∝1/n (c) v = nh/2πmr Relation between vn and v1:-vn = v1/n Radius of electron:- r= n2h2/4π2kmZe2 So, r∝n2 For, C.G.S system (k = 1), r = n2h2/4π2mZe2 S.I (k = 1/4πε0), r =(ε0/π) (n2h2/mZe2) Kinetic energy of the electron:- It is the energy possessed by the electron by virtue of its motion in the orbit. K.E = ½ mv2 = ½ k (Ze2/r) Potential energy:- It is the energypossessed by the electronby virtue of its position near the nucleus. P.E = -k (Ze2/r ) Total energy:- W= K.E + P.E W=- ½ k (Ze2/r) = -k2 2π2Z2me4/n2h2 For, C.G.S (k = 1), W = - [2π2Z2me4/n2h2] For, S.I. ( k = 1/4πε0), W = - (1/8ε02) [Z2me4/n2h2] Since, W∝1/n2, a higher orbit electron possesses a lesser negative energy (greater energy) than that of a lower orbit electron. Frequency, wavelength and wave number of radiation:- Frequency, f = k2[2π2Z2me4/h3] [1/n12 – 1/n22] Wave number of radiation, Here R is the Rydberg’s constant and its value is, R= k2 [2π2Z2me4/ch3] Bohr’s theory of hydrogen atom (Z=1):- (a) Radius of orbit:- r= n2h4/4π2me2 (C.G.S) r= (ε0/π) (n2h2/me2) (S.I) (b) Energy of electron:- W= 2π2me4/n2h2 (C.G.S) W =(1/8ε0)[me4/n2h2] (c) Frequency, wavelength and wave number of radiation:- C.G.S:- k =1 and Z=1 Frequency= f=2π2me4/h3 [1/n12 – 1/n22] Wave number = 1/λ = 2π2me4/ch3 [1/n12 – 1/n22] S.I:- k =1/4πε0 and Z=1 Frequency= f = (1/8ε0) (me4/h3)[1/n12 – 1/n22] Wave number = 1/λ = (1/8ε02) (me4/ch3)[1/n12 – 1/n22] Rydberg’s constant:- R=k2 =2π2z2 me4/ch3 For hydrogen atom, Z = 1, R = RH = k2 (2π2 me4/ch3). For C.G.S system (k=1), RH = 2π2 me4/ch3 For S.I system (k=1/4πε0), RH = (1/8ε02) (me4/ch3) Wave number, 1/λ = RH [1/n12 – 1/n22] Hydrogen Spectrum:- (a) For Lyman series:- 1/λ = R [1– 1/n2], n = 2,3,4…..∞ (b) For Balmer series:- 1/λ = R [1/22 – 1/n2], n =3,4,5…..∞ (c) For Paschen series:-1/λ = R [1/32 – 1/n2], n =4,5,6…..∞ (d) For Brackett series:-1/λ = R [1/42 – 1/n2], n =5,6,7…..∞ (e) P-fund series:-1/λ = R [1/52 – 1/n2], n =6,7,8…..∞ Series limits (λmin):- (a) Lyman:- λmin = 912 Å (b) Balmer:-λmin = 3645 Å (c) Paschen:- λmin = 8201 Å Energy levels of hydrogen atom:- W = -k22π2me4/n2h2 For, n=1, W1 = -13.6 eV For the first excited state, n=2, W2 =W1/4 = (-13.6/4) eV = -3.4 eV For the second excited state, n=3, W3 =W1/9 = (-13.6/9) eV = -1.51 eV Similarly, for other excited states, W4 = -0.85 eV and W5 = -0.54 eV Number of emission lines from excited state:-n = n(n-1)/2 Ionization energy:- - E1 = +(13.6Z2)eV (a) For H-atom, I.E = 13.6 eV (b) For He+ ion, I.E = 54.4 eV (c) For Li++ ion, I.E = 122.4 eV Ionization potential:- (a) For H-atom, I.P = 13.6 eV (b) For He+ ion, I.P = 54.42 eV