Formelsamling Formelsamlingens konstanter och tabellvärden antas i uträkningar vara exakta värden. Avogadros tal NA = 6,022 · 1023 1/mol Gravitationskonstanten γ = 6,6742 · 10−11 Nm2 /kg2 Elektronen laddning e = −1,602 · 10−19 C Kvicksilvers densitet 13600 kg/m3 Faradays tal F = 96,5 · 103 C/mol Molvolymen för idealgaser Vm = 22,41 `/mol (NTP) Densiteten för torr luft 1,29 kg/m3 (NTP) Hörseltröskelns intensitet I0 = 10−12 W/m2 Normalt lufttryck 1 atm = 101325 Pa Gravitationsaccelereringen orsakad av jordens dragkraft g = 9,81 m/s2 0 ℃ = 273,15 K Plancks konst. h = 6,626 · 10−34 Js = 4,1357 · 10−15 eVs Stefan-Boltzmans konst. σ = 5,67 · 10−8 W/(m2 · K4 ) Permittivitet för vakuum 0 = 8,85 · 10−12 F/m Ljusets hastighet c = 3,0 · 108 m/s Vattnets densitet 1,0 · 103 kg/m3 (0 ℃ − 100 ℃) Blodets densitet 1050 kg/m3 Vattnets förångningsvärme 2260 kJ/kg Vattnets autoprotolys Kw = 1,008 · 10−14 (mol/`)2 Vattnets specifika värmekapacitet 4,19 kJ/(K · kg) Allmänna gaskonstanten R = 8,314 J/(mol · K) Ljudets hastighet i luft 343 m/s k = 1 för en svart kropp 1 eV = 1,602 · 10−19 J 1 curie = 1 Ci = 3,7 · 1010 Bq 1 kwh = 3,6 MJ proton: mp = 1,6726586 · 10−27 kg neutron: mn = 1,6749543 · 10−27 kg elektron: me = 9,109 · 10−31 kg atomimassaenhet: mu = 1,6605655 · 10−27 kg mp = 1,0072825 mu mn = 1,0086650 mu ax2 + bx + c = 0 √ −b ± b2 − 4ac x= 2a [A− ][HB+ ] K= [HA][B] [A− ][H3 O+ ] Ka = [HA] − [A ][H+ ] Ka = [HA] [A− ] pH = pKa + lg [HA] [A− ] 1 = − (pK [HA] + [A ] 1 + 10 a −pH) [HA] 1 = − (pH−pK a) [HA] + [A ] 1 + 10 L1 I = I0 e −cd A = lg(I0 /I) A = cd [H3 O+ ] = p Ka · Ctot p = ρgh U = RI, P = UI c = Hp0 A = 4πr2 V = (4/3)πr3 Jd KD =P = ∆c ∆x P = φD/∆x RT cs ∆V = − ln u ZF c dc F dV J = −D + Zc dx RT dx ! RT PNa cuNa + PK cuK + PCl csCl ∆V = Vs − Vu = ln F PNa csNa + PK csK + PCl cuCl csK cu = Cl u cK csCl (cuCl + |Zp |cup )c0Cl = csK csCl dE I = Cm + gNa (E − ENa ) + gK (E − EK ) + g` (E − E` ) dt sin(α) λ1 c1 n2 = = = = n21 sin(β) λ2 c2 n1 1 1 1 + = a b f h λ= mv F = q(v × B); F = qvB sin(α) B = µ0 I/(2πr) F = Q1 Q2 /(4π0 r2 ) F = QE, E = U/d F = mω 2 r = V (ρm − ρn )ω 2 r v = F/f = V (ρm − ρn )ω 2 r/f W = 1 /2 Jω 2 1 v = QE 6πrη Es = [Zmp + N mn − mγ ]c2 A = λN = λN0 e−λt = A0 e−λt lg A = lg A0 − (lg e)λt ln(2) T1 /2 = λ λef = λfys + λbiol Tf Tb Tf Te Te = , Tb = Tf + Tb Tf − Te L2 A = A1 e−λ1 t + A2 e−λ2 t f2 = [(n2 − n1 )r + n1 r]/(n2 − n1 ) = f1 + r I = I0 e−µx H = wR D; E= XX R wR wT D T ; q v= q X WT = 1 T E = hf = hc/λ; √ f = 1/(2π LC) v= XL = 2πf L H T = wR D T E( eV) = 1240/λ( nm) pV = nRT p2 V2 p1 V1 = T1 T2 V = V0 (1 + αV ∆T ) γRT /M p = p0 (1 + αp ∆T ) E/ρ Q = cp m∆T I0 = 10−12 W/m2 β = 10 lg(I/I0 ) R = 10 lg(P1 /P2 ) = 10 lg(1/τ ) τ1 A1 + τ2 A2 + . . . τ= A c c±v f = f0 ; f = f0 c±v c 2 F = mv /r T = (f1 /f2 ) = (n1 /n2 ) q 4π 2 (r/a) 4π 2 F = mω 2 r = 2 mr T m1 m2 F =γ 2 r λAθ φ= d λθ q= d φ = hAθ θ = T1 − T2 P P = σT 4 ; = kσT 4 A A h = 1 /2 gt2 v = v0 + gt h = v0 t + 1 /2 gt2 ω = ω0 + αt ϕ = ϕ0 + ω0 t + 1 /2 αt2 T = 2π/ω n = 1/T an = v 2 /r F = mv 2 /r = mω 2 r = (4π 2 /T 2 )mr y(x, t) = ymax sin(ωt − kx) p(x, t) = pmax cos(ωt − kx) I = Φ/ω = Φtot /4π E = Φ/A L = I/A; [L] = cd/m2 = 1 Nit = 1 nitti L = Ig /(A cos()) (n1 /a) + (n2 /b) = (n2 − n1 )/r W = γ∆A W = F ∆` 1 / mv 2 Ek 2 = = 1 /2 ρv 2 V V Ep mgh = = ρgh V V Fs W F = = p= A As V q c= (∆p/∆V )(V /p) F = (EA/`)(∆`) F = N ABI sin(α) R = ∆p/qv = 8ηL/(πr4 ) PRU = ∆p( mmHg)/qv ( ml/s) PVR = 80(P Am − LAm )/Vp SVR = 80(AOm − RAm )/Vp π∆pR4 8ηL ρvR Re = η 2 (ρ − ρ0 )gr2 v= 9 η W = Fs qv = Ep = mgh p = mv Ek = 1 /2 mv 2 Er = 1 /2 Jω 2 P = W/∆t η = Wa /Wo η = (Wa /∆t)/(Wo /∆t) = Pa /Po µ(x, y, z) − µvesi T T -luku = 1000 µvesi M =F ·r Epot = qU XC = 1/(2πf C) J= X ms2 Aminosyrorna NH2 NH2 COOH O NH H2 N COOH Alanin, Ala, A H2 N NH Arginin, Arg, R COOH H2 N O COOH O Glutaminsyra, Glu, E Glutamin, Gln, Q H COOH H2 N Leucin, Leu,L COOH Lysin, Lys, K, HO Serin, Ser, S 1 I H [1] 2 II 3 IIIb COOH N Histidin, His, H NH COOH Fenylalanin, F Phe, Prolin, Pro, P NH2 HO NH2 NH2 COOH OH 6 VIb Isoleucin, Ile, I COOH Metionin, Met, M COOH Treonin, Thr, T 5 Vb COOH NH2 COOH 4 IVb NH2 COOH NH2 COOH COOH Cystein, Cys, C NH2 HN NH2 HN NH2 COOH HS Glysin, Gly, G S NH2 Asparaginsyta, Asp, D COOH NH2 NH2 NH2 HO NH2 NH2 COOH O Asparagin, Asn, N NH2 HO NH2 7 VIIb Tryptofan, Trp, W 8 9 VIIIb 10 Tyrosin, Tyr, Y 11 Ib 12 IIb COOH Valin, Val, V 13 III 14 IV 15 V 16 VI 17 VII B [5] C [6] N [7] O [8] F [9] 1,0079 Li [3] 18 VIII He [2] 4,0026 Be [4] Ne [10] 6,9412 9,0121 10,811 12,010 14,006 15,999 18,998 20,179 Na [11] Al [13] Mg [12] 22,989 24,305 K [19] Ca [20] Si [14] P [15] S [16] Cl [17] Ar [18] 26,981 28,085 30,973 32,065 35,453 39,948 Sc [21] Ti [22] V [23] Cr [24] Mn [25] Fe [26] Co [27] Ni [28] Cu [29] Zn [30] Ga [31] Ge [32] As [33] Se [34] Br [35] Kr [36] 39,098 40,078 44,955 47,867 50,941 51,966 54,938 55,845 58,933 58,693 63,546 65,409 69,723 72,641 74,921 78,963 79,904 83,798 Rb [37] Ru [44] Sr [38] Y [39] Zr [40] Nb [41] Mo [42] Tc [43] Rh [45] Pd [46] Ag [47] Cd [48] In [49] Sn [50] Sb [51] Te [52] I [53] Xe [54] 85,467 87,621 88,905 91,224 92,906 95,942 98,906 101,07 102,90 106,42 107,86 112,41 114,81 118,71 121,76 127,60 126,90 131,29 Cs [55] Os [76] Ba [56] La [57] Hf [72] Ta [73] W [74] Re [75] Ir [77] Pt [78] Au [79] Hg [80] Tl [81] Pb [82] Bi [83] Po [84] At [85] Rn [86] 132,90 137,32 138,90 178,49 180,94 183,84 186,20 190,23 192,21 195,08 196,96 200,59 204,38 207,21 208,98 208,98 209,98 222,01 Fr [87] Hs Mt Ds Rg Uub Uut Uuq Uup Uuh Uus Uuo [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] Ra [88] Ac [89] Rf Db Sg Bh [104] [105] [106] [107] 223,01 226,02 227,02 261,10 262,11 266,12 264,12 Lantanoider Aktinoider Ce [58] Pr [59] Nd [60] Pm [61] Sm [62] Eu [63] Gd [64] Tb [65] Dy [66] Ho [67] Er [68] Tm [69] Yb [70] Lu [71] 140,11 140,90 144,24 146,91 150,36 151,96 157,25 158,92 162,50 164,93 167,25 168,93 173,04 174,96 Th [90] Np [93] Pa [91] U [92] 232,03 231,03 238,02 Pu [94] Am [95] Cm [96] Bk [97] Cf [98] Es [99] Fm Md No Lr [100] [101] [102] [103] 237,04 244,06 243,06 247,07 247,07 251,07 252,08 257,09 258,09 259,10 260,10