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♦️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

✡️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. @ET_STUDY_NOTES

✅ 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: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes

📚 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: @Ethio_Educational_News 📚JOIN: @EUEE_TIPS 📚JOIN: @Et_Study_Notes