(1) Intensity Level $$ L = 10 log_10(I/I_0) \text"(in dB)" $$ where, L is loudness (2) Sabine’s Formula $$ T = {0.165 V}/{aS} $$ where, T is Reverberation time V is Volume of hall S is Total area a is Absorption coefficient Also, $ A = ∑↙{i=1}↖n aS $ where, A is Effective absorbing area
(1) asinθ = nλ (Direction of minima for single silt) where, a = slit width AB n = order of spectrum λ = Wavelength of incident light θ = Angle of diffraction (2) $ asinθ’= (n+1/2)λ, $ (Direction of secondary maxima for single slit) where, a = slit width AB n = order of spectrum λ=Wavelength of incident light (3) (a+b) sinθ = mλ, (Direction of maxima for grating) where, a = slit width b = opaque space m = order of spectrum λ = wavelength of incident light (a+b) = ...
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(1) Intensity of interference pattern, $$I_{max} / I_{min} = (a+1)^2 / (a-1)^2 where, a>1$$ where, $$I_{max} = \text"Maximum Intensity" $$ $$ I_{min} = \text"Minimum Intensity" $$ (2) Reflected light, (i) For maxima or bright fringe, $$ 2μtcosr = (2n-1) λ/2 $$ where, n = 1,2,3,… μ = Refractive index λ = Wavelength of light r = Angle of refraction (ii) For minima or dark fringe, $$ 2μtcosr = nλ $$ n = 0,1,2,3,.. (3) Fringe width, $$ ω = λ/{2μθ} $$ where, λ = Wavelength of light θ = Angle of ...
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For a reaction, aA + bB -> cC + dD Average rate = -$1/a {Δ[A]}/{Δt}$ = – $1/b {Δ[B]}/{Δt}$ = – $1/c {Δ[C]}/{Δt}$ = -${Δ[D]}/{Δt}$ Rate law: Rate = $k [A]^a * [B]^b$ k = ${2.303}/t log_{10} {[A]_o}/{[A]_t}$ (For first order reaction) $t_{1/2} = {0.693}/k$ (For first order reaction) $k = {[A]_o – [A]_t}/{t}$ (For zero order reaction) $t_{1/2} = {[A]_o}/{2k}$ (For zero order reaction) $k = A e^{-{Ea}/{RT}}$ (Arrhenius equation) $log_{10}k = log_{10}A – {E_a}/{2.303 RT}$ $log_{10} {k_2}/{k_1} = {E_a (T_2 – T_1)}/{2.303 R T_1 T_2}$
Electrical Conductance (G): $1/R = I/V$ $R = ρ l/a$ Conductivity of Conductor (k) $G l/a = 1/ρ$ Molar Conductivity $⋀ = k/c = {\text"electrolytic conductivity"}/{\text"molar concentration"}$ ⋀ = k V $⋀ = ⋀_o – a √c$ c -> concentration ; $⋀_o$ -> molar conductivity at zero concentration or infinite dilution a -> constant Kohlrausch Law: $⋀_o = λ^o_+ + λ^o_-$ where $λ^o_+$ & $λ^o_-$ are molar conductivities of cation and anion at zero concentration Degree of dissociation of weak electrolyte: $α = {⋀}/{⋀_o}$ Dissociation constant: $k = {α^2 C}/{1 – α}$ $k = {⋀^2 C}/{⋀_o (⋀_o – ⋀)}$ Cell ...
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W = -PΔV (For expansion) W = PΔV (For compression) $W_{max} = -2.303 nRT log_{10}{V_2}/{V_1}$ $W_{max} = -2.303 nRT log_{10}{P_1}/{P_2}$ ΔU = q + W ΔH = ΔU + PΔV ΔH = ΔU + ΔnRT Hess’s Law: ΔH = Δ$H_1$ + Δ$H_2$ + Δ$H_3$ ΔS = ${q_{rev}}/{T} = {ΔH}/{T}$ ΔG = ΔH – TΔS $ΔG^{o} = -2.303 RT log_{10}K$ (i)ΔG = 0, the system is at equilibrium (ii)ΔG < 0, the system is spontaneous (iii)ΔG > 0, the process is non-spontaneous Δn = [No. of moles of gaseous products] – [No. of moles of gaseous reactants] $q_p = ΔH$ and ...
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Number of moles, $n = W/M$ mol Molarity = $n/V$ mol $dm^{-3}$ (or M) Normality = ${\text"gram eq."}/{V}$ gram eq. $dm^{-3}$ (or N) Molality = $n/{\text"Wt. of solvent in kg"}$ mol $kg^{-1}$ (or m) Raoult’s law: $P_{soln} = x_{1} P_o$ ${P_{o} – P}/{P_o} = {W_{2} M_{1}}/{W_{1} M_{2}}$ $ΔT_b = K_b m$ and $Δ T_f = K_f m$ $ΔT_b = K_b * {1000 W_2}/{W_1 M_2}$ $ΔT_f = K_f * {1000 W_2}/{W_1 M_2}$ At constant temperature: ${π_2}/{π_1} = {C_2}/{C_1}$ At constant concentration: ${π_2}/{π_1} = {T_2}/{T_1}$ van’t Hoff equation: 1. π = CRT 2. π = $n/V$ RT 3. π = ${WRT}/{MV}$ van’t ...
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Number of atoms in the unit cell: $\table \text"Unit Cell",scc,bcc,fcc,hcp;\text"No. of atoms",1,2,4,3$ Packing efficiency $\table scc,bcc,fcc,hcp;52.4%,68%,74%,74%$ Note: 1. Number of tetrahedral voids = 2 Number of atoms 2. Number of octahedral voids = Number of atoms Relation between radius (r) of an atom and edge length (a) of cubic unit cell $\table scc,bcc,fcc;r = a/2, r={√3}/{4} a, r = {a}/{2√2}$ Density of the crystal $d = {z * M}/{a^{3} * N_A}$ where, z = Number of atoms in unit cell M = Atomic Mass a = Edge length of unit cell $N_A$ = Avogadro Number Note 1 m = 10 ...
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y = f(x), point P(a,f(a)) Tangent equation: y – f(a) = f'(a) (x-a) Slope of normal: -${1}/{{dy}/{dx}}$ Formula of approximation: f(a+h) ≑ f(a) + h . f'(a) Rolle’s Theorem: Function f is continuous & differentiable on (a,b) and f(a) = f(b) Then there exists at least one point c∊ (a,b) such that f'(c) = 0 Langrange’s Mean value theorem: ${f(b) – f(a)}/{b – a} = f'(c) $ A function: Increasing -> f'(x) > 0 , and maximum -> f'(c) = 0 & f”(c) f'(x) < 0 , and minimum -> f'(c) = 0 & f”(c) > 0 1st Derivative Test: ...
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$\lim↙{x→0} {sinx}/{x} = 1$ $\lim↙{x→0} {tanx}/{x} = 1$ $\lim↙{x→0} cosx = 1$ $\lim↙{x→0} {a^x – 1}/{x} = log a$ $\lim↙{x→0} log (1+x)^{1/x} = log e$ $\lim↙{x→0} (1+x)^{1/x} = e $ Note: Whenever there is a role of π with x e.g. ${sinπx}/{x – 1} + a$ Put x – 1 = h i.e. Make denominator singular