WORLD CRYPTO AND NET

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📚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 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 @Educational_Question @Et_Study_Notes @Oromia_Educational_News @AmboIfaBoru @Bright_codes_academy

🛑Structure of the Atom🛑 ➖By 1900, it was discovered that the atom was not a simple, indivisible particle, but rather it contains sub-atomic particles. ➖J.J. Thomson discovered the sub-atomic particle namely ‘electron.’ ➖J.J. Thomson was the first person who proposed a model for the structure of an atom. ➖In 1886, E. Goldstein discovered the presence of new radiations in a gas discharge and named them canal rays. ➖Another positively charged sub-atomic particle was discovered with experiments of canal rays and named it proton. 🧿Thomson’s Model of Atom ➖Thomson proposed that an atom consists of a positively charged sphere and the electrons (negative charge) are embedded in it (as shown in the image given below). ➖Further, Thomson said that the negative and positive charges are equal in magnitude. Thus, the atom as a whole is electrically neutral. 🧿Rutherford’s Model of Atom ➖E. Rutherford is popular as the ‘Father’ of nuclear physics. ➖Rutherford is largely known for his work on radioactivity and the discovery of the nucleus of an atom with the gold foil experiment (as shown in the image given below. ➖Rutherford said that in an atom, there is a positively charged center known as the nucleus. ➖Rutherford said that nearly all the mass of an atom exists in in the nucleus. ➖According to Rutherford, the electrons revolve around the nucleus in well-defined orbits. 🧿Bohr’s Model of Atom ➖Neils Bohr further extended Rutherford’s model and improved his drawbacks. ➖According to Bohr, only certain special orbits known as discrete orbits of electrons, are allowed inside the atom. ➖Bohr said that electrons do not radiate energy while revolving in discrete orbits. ➖Bohr named orbits or shells as energy levels. ➖Bohr represented these orbits or shells are by the letters K, L, M, N,… or the numbers, n = 1,2,3,4,…. 🧿Neutron ➖In 1932, J. Chadwick discovered a new sub-atomic particle i.e. neutron. ➖Neutron has no charge and a mass nearly equal to that of a proton. ➖Neutrons are present in the nucleus of all atoms, except hydrogen. 🧿Electrons Distributed in Different Orbits (Shells) ➖The maximum number of electrons that can be present in a shell is given by the formula 2n2. ➖‘n’ is the orbit number or energy level index, i.e. 1, 2, 3,…. ➖According to the given formula − First orbit i.e. K-shell will be = 2 × 12 = 2 Second orbit i.e. L-shell will be = 2 × 22 = 8 Third orbit i.e. M-shell will be = 2 × 32 = 18 Fourth orbit i.e. N-shell will be = 2 × 42 = 32 ➖Likewise, the maximum number of electrons that can be accommodated in the outermost orbit is 8. ➖Electrons are not filled in a given shell, unless the inner shells are filled. It means, the shells are filled in a step-wise manner; starting from inner shell to outer shell. 🧿Valence ➖The electrons, those are present in the outermost shell of an atom, are known as the valence electrons. ➖According to Bohr-Bury model, the outermost shell of an atom can have a maximum of 8 electrons. 🧿Atomic Number ➖The total number of protons, present in the nucleus of an atom, is known as atomic number. ➖The number of protons of an atom determines the atomic number. ➖Atomic number is denoted by ‘Z’. ➖Protons and neutrons collectively are known as nucleons. 🧿Mass Number ➖The sum of the total number of protons and neutrons, present in the nucleus of an atom, is known as mass number. 🧿Isotopes ➖The atoms of the same element, having the same atomic number but different mass numbers, is known as isotopes. E.g. Hydrogen atom has three isotopes namely protium, deuterium, and tritium. ➖The chemical properties of isotopes of an atom are similar but their physical properties are different. 🧿Isobars ➖Atoms of different elements with different atomic numbers, which have the same mass number, are known as isobars. E.g. calcium’s atomic number is 20and argon’s atomic number is 18; further, the number of electrons in these atoms is different, but the mass number of both these elements is 40. 📚@Educational_Question 📚@Et_Study_Notes 📚@Oromia_Educational_News 📚@AmboIfaBoru 📚@Bright_codes_academy

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🔥Increasings or Decreasing Order🔥 🔴 01. Melting point= Li > Na > K > Rb > Cs 🔴 02. Colour of the flame= Li-Red, Na-Golden, K-Violet, Rb-Red, Cs-Blue, Ca-Brick red, Sr-Blood red, Ba-Apple green 🔴 03. Stability of hydrides = LiH > NaH > KH > RbH> CsH 🔴 04. Basic nature of hydroxides= LIOH < NaOH < KOH < RbOH < CsOH 🔴 05. Hydration energy= Li> Na > K> Rb > Cs 🔴 06. Reducing character= Li > Cs > Rb > K > Na 🔴 07. Stability of +3 oxidation state= B> Al > Ga > In > T1 🔴 08. Stability of +1 oxidation state= Ga < In < TI 🔴 09. Basic nature of the oxides and hydroxides= B< Al< Ga < In < TI 🔴 10. Relative strength of Lewis acid= BF3 < BCl3 < BBr3 < BI3 🔴 11. Ionisation energy= B> Al <Ga > In <TI 🔴 12. Reactivity= C<Si< Ge < Sn <Pb 🔴 13. Metallic character= C< Si < Ge < Sn < Pb 🔴 14. Acidic character of the oxides= Co2 > SiO2 > Ge02 > SnO2 > PbO2 🔴 15. Reducing nature of hydrides= CH4 < SiH4 < GeH4 < SnH4 < PbH4 🔴 16. Thermal stability of tetrahalides= CCl4> SiCl4> GeCl4> SnCl4 > PbCl4 🔴 17. Oxidising character of M+4 species= GeCl4 < SnCl4 < PbCl4 🔴 18. Ease of hydrolysis of tetrahalides= SiCl4 < GeCl4 < SnCl4 < PbCI4 🔴 19. Acidic strength of trioxides= N203 > P2O3 > As2O3 🔴 20. Acidic strength of pentoxides= N2O2 > P2O2> As202 > Sb2O2 > Bi‌202 🔴 21. Acidic strength of oxides of nitrogen= N2O < NO <N2O3 <N2O4 < N2O5 🔴 22. Basic nature/ bond angle/ thermal stability and dipole moment of hydrides= NH3 > PH3 > AsH3 > SbH3 > BiH3 🔴 23. Stability of trihalides of nitrogen= NF3 > NCl3 > NBr3 🔴 24.Lewis base strength= NF3 <NCl3 <NBr3 < NI3 🔴 25. Ease of hydrolysis of trichlorides= NCl3 > PCI3 > AsCl3 > SbCl3 > BiCl3 🔴 26. Lewis acid strength of trihalides of P, As, and Sb= PCl3 > ASCl3 > SbCl3 🔴 27. Lewis acid strength among phosphorus trihalides PF3 > PCl3 > PBr3 > PI3 🔴 28. Melting and boiling point of hydrides= H2O > H2Te > H2Se >H2S 🔴 29. Volatility of hydrides= H2O < H2Te < H2Se < H2S 🔴 30. Reducing nature of hydrides= H2S < H2Se < H2Te 🔴 31. Covalent character of hydrides= H2O < H2S < H2Se < H2Te 🔴 32. The acidic character of oxides (elements in the same oxidation state)= SO2 > SeO2 > TeO2 > PoO2 SO3 > SeO3 > TeO3 🔴 33. Acidic character of oxide of a particular element (e.g. S)= SO < SO2 < SO3 SO2 > TeO2 > SeO2 > PoO2 🔴 34. Bond energy of halogens= Cl2 > Br2 > F2 > I2 🔴 35. Solubility of halogen in water = F2 > Cl2 > Br2 > I2 🔴 36. Oxidising power= F2 > Cl2 > Br2 > I2 🔴 37. Enthalpy of hydration of X ion= F- > Cl- > Br- >I- 🔴 38. Reactivity of halogens:= F> Cl> Br > I 🔴 39. Ionic character of M-X bond in halides = M-F > M-Cl > MBr > M-I 🔴 40. Reducing character of X ion:= I- > Br- > Cl- > F- 🔴 41. Acidic strength of halogen acids= HI > HBr > HCI > HF 🔴 42. Reducing property of hydrogen halides = HF < HCL < HBr < HI 🔴 43. Oxidising power of oxides of chlorine = Cl2O > ClO2 > Cl206 > Cl2O7 🔴 44. Decreasing ionic size= 02- > F- > Na+ > Mg2+ 🔴 45. Increasing acidic property= Na2O3 < MgO < ZnO< P205 🔴 46. Increasing bond length= N2 <02 < F2 < CL2 🔴 47. Increasing size= Ca2+ < Cl- < S2- 🔴 48. Increasing acid strength= HClO < HClO2 < HClO3 < HClO4 🔴 49. Increasing oxidation number of iodine= HI< I2 <ICl <HIO4 🔴 50. Increasing thermal stability= HOCl < HOClO < HOClO2 < HOClO3 Join our Educational Channels: ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Educational_Question 📚JOIN: @Et_Study_Notes 📚JOIN: @Oromia_Educational_News 📚JOIN: @AmboIfaBoru 📚JOIN: @General_questions_always

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].

✅ 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 our Educational Channels: ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Educational_Question 📚JOIN: @Et_Study_Notes 📚JOIN: @Oromia_Educational_News 📚JOIN: @AmboIfaBoru 📚JOIN: @General_questions_always

✅ 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 our Educational Channels: ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Educational_Question 📚JOIN: @Et_Study_Notes 📚JOIN: @Oromia_Educational_News 📚JOIN: @AmboIfaBoru 📚JOIN: @General_questions_always

♦️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♦️(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

♦️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 our Educational Channels: ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Educational_Question 📚JOIN: @Et_Study_Notes 📚JOIN: @Oromia_Educational_News 📚JOIN: @AmboIfaBoru 📚JOIN: @General_questions_always

🔰 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 our Educational Channels: ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Educational_Question 📚JOIN: @Et_Study_Notes 📚JOIN: @Oromia_Educational_News 📚JOIN: @AmboIfaBoru 📚JOIN: @General_questions_always

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✡️Notes on Atomic Physics✡️ e/m of an electron (Thomson Method):- (a) e/m of a particle is called the specific charge of the particle. e/m = v/rB Here, r is the radius of curvature, B is the strength of magnetic field, v is the velocity, e is the charge on cathode ray particle and m is the mass. (b) v = E/B Electric field:- E = V/d Photo electric effect:- Photo-electric effect is the phenomenon of emission of electrons from the surfaces of certain substances, mainly metals, when light of shorter wavelength is incident upon them. Effect of collector’s potential on photoelectric current:- (a) Presence of current for zero value potential indicates that the electrons are ejected from the surface of emitter with some energy. (b) A gradual change in the number of electrons reaching the collector due to change in its potential indicates that the electrons are ejected with a variety of velocities. (c) Current is reduced to zero for some negative potential of collector indicating that there is some upper limit to the energy of electrons emitted. (d) Current depends upon the intensity of incident light. (e) Stopping potential is independent of the intensity of light. Effect of intensity of light:- The photoelectric currentis directly proportional to theintensity of incident radiation. Effect of frequency of light:- (a) Stopping potentialdepends upon thefrequency of light. Greater the frequency of light greater is the stopping potential. (b) Saturation current is independent of frequency. (c) Threshold frequency is the minimum frequency, that capable of producing photoelectric effect. Laws of Photoelectricity:- (a) Photoelectric effect is an instantaneous process. (b) Photoelectric current is directly proportional to the intensity of incident light and is independent of its frequency. (c) The stopping potential and hence the maximum velocity of the electrons depends upon the frequency of incident light and is independent of its frequency. (d) The emission of electrons stops below a certain minimum frequency known as threshold frequency. Energy contained in bundle or packet:- E = hf = hc/λ Here h is the Planck’s constant and f is the frequency. Work function:- It is defined as the minimum energy required to pull an electron out from the surface of metal. It is denoted by W0. Einstein’s equation of photoelectric effect:- (a) ½ mvmax2 = hf – W0 (b) ½ mvmax2 = hf – hf0 = h(f- f0) = h [c/λ – c/λ0] (c) eV0 = hf - W0 (d)V0 = [(h/e)f] – [W0/e] Here f0 is threshold frequency. Threshold frequency (f0):- f0 = work function/h = W/h Maximum kinetic energy of emitted photo electrons:- ?Kmax= ½ mvmax2 = eV0 Threshold wavelength:- λ0 = c/f0 = hc/hf0 = hc/W Slope of V0~ v graph:- Slope= h/e Rest mass of photon = 0, Charge = 0 Energy of photon:- E = hf = hc/λ Momentum of photon:- p = E/c = h/λ = hf/c Mass od photon:- m = E/c2 = h/cλ = hf/c2 For electron, λe = [12.27/√V]Å For proton, λp = [0.286/√V]Å For alpha particle, λα = [0.286/√V]Å For particle at temperature T, λ = h/√3mKT (E = 3/2 KT) The wavelength of electron accelerated by potential difference of V volts is:- λe= [12.27/√V]Å Number of photons:- (a) Number of photons per sec per m2, np = Intensity/hf (b) Number of photons incident per second, np = Power/hf (c) Number of electrons emitted per second = (efficiency per surface)× (number of photons incident per second) Compton wave length:- (a) λc = h/m0c Here h is the Planck’s constant, m0 is the rest mass of electron and c is the speed of light. (b) Change in wavelength:- λ' – λ =λc (1-cos?) de Broglie wavelength (λ):-λ = h/mv = h/√(2mE) = h/√(2meV) In accordance to Bohr’s postulate of atomic structure, the angular momentum of an electron is an integral multiple of h/2π. So, mvr = nh/2π Bragg’s diffraction law:- 2dsinθ = nλ Here λ is the wavelength of electron and d is distance between the planes. Rutherford’s atomic model (α-particle scattering):- (a) N(θ) ∝ cosec4(θ/2) (b) Impact parameter, b = [(Ze2) (cot θ/2)]/[(4πε0)E] Here, E = ½ mv2 = KE of theα particle.

✅ Atomic and Molecular Masses ➖Atomic Mass: Mass of an atom. Reported in atomic mass unit “amu” or unified mass “u” One atomic mass unit i.e. amu, is the mass exactly equal to one-twelfth the mass of one carbon-12 atom. ➖Molecular Mass: Mass of a molecule of covalent compound. It is equal to the sum of atomic masses of all the elements present in the molecule. Formula Unit Mass Mass of a molecule of an ionic compound It is also equal to the sum of atomic masses of all the elements present in the molecule ✅ Mole Concept: ➖Mole: Unit of amount of substance. One mole amount of substance that contains as many particles or entities as there are atoms in exactly 12 g of the 12C isotope. ➖Molar mass: Mass of one mole of a substance in gram Molar mass in gram in numerically equal to atomic/molecular/formula mass in amu or u. Join our Educational Channels: ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Educational_Question 📚JOIN: @Et_Study_Notes 📚JOIN: @Oromia_Educational_News 📚JOIN: @AmboIfaBoru 📚JOIN: @General_questions_always

📚 Some Basic Concepts of Chemistry 📚 Matter: Anything that exhibits inertia is called matter. The quantity of matter is its mass. Classification of Matter:- Based on chemical composition of various substances. 📍Elements: ➖It is the simplest form of the matter. ➖Smallest unit of an element is known as atom. ➖Total number of the known elements is 118 out of which 98 elements occur naturally and 20 are formed by artificial transmutation. ➖Examples: Na, K, Mg. Al, Si, P, C, F, Br etc. 📍Compound: ➖It is a non-elemental pure compound. ➖Formed by chemical combination of two or more atoms of different elements in a fixed ratio. ➖Examples: H2O, CO2, C6H12O6 etc. 📍Mixture: ➖Formed by physical combination of two or more pure substances in any ratio. ➖Chemical identity of the pure components remains maintained in mixtures. ➖Homogeneous mixtures are those whose composition for each part remains constant. ➖Example, Aqueous and gaseous solution. ➖Heterogeneous mixtures are those whose composition may vary for each and every part. ➖Example, Soil and concrete mixtures. 🧩Dalton’s Atomic Theory: ➖Every matter consists of indivisible atoms. ➖Atoms can neither be created nor destroyed. ➖Atoms of a given element are identical in properties ➖ Atoms of different elements differ in properties. ➖Atoms of different elements combine in a fixed ratio to form molecule of a compound. 🧩Precision and Accuracy: ➖Precision: Closeness of outcomes of different measurements taken for the same quantity. ➖Accuracy: Agreement of experimental value to the true value 🧩Laws of Chemical Combination: ➖Law of conservation of mass: “For any chemical change total mass of active reactants are always equal to the mass of the product formed” ➖Law of constant proportions: “A chemical compound always contains same elements in definite proportion by mass and it does not depend on the source of compound”. ➖Law of multiple proportions: “When two elements combine to form two or more than two different compounds then the different masses of one element B which combine with fixed mass of the other element bear a simple ratio to one another” ➖Law of reciprocal proportion: “ If two elements B and C react with the same mass of a third element (A), the ratio in which they do so will be the same or simple multiple if B and C reacts with each other”. ➖Gay Lussac’s law of combining volumes: “At given temperature and pressure the volumes of all gaseous reactants and products bear a simple whole number ratio to each other”. Join our Educational Channels: ▬▬▬▬▬▬▬▬▬▬▬▬▬ 📚JOIN: @Educational_Question 📚JOIN: @Et_Study_Notes 📚JOIN: @Oromia_Educational_News 📚JOIN: @AmboIfaBoru 📚JOIN: @General_questions_always