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Biophysics > Biophysics Formulae > Flashcards

Biophysics Formulae Flashcards

1
Q

De broglie’s equation (wave)

A

λ = h/p = h/√(2mE)

Where…

h = planck’s constant = ( 6.63*10^-34 j/s)

p= momentum

λ=wave length

E = energy m = electron mass

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2
Q

Energy of a photon relating to frequency

A

E = hf = h(c/λ)

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3
Q

Max number of electron in a shell (n)

A

2n2

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4
Q

Max number of electron in a subshell (s)

A

4l+2

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5
Q

Magnetic quantum number

A

2l+1

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6
Q

Spin quantum number

A

+- 1/2

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7
Q

Ionization

A

Eb = -E

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8
Q

Ionization: Einstein’s equation for photoelectric effect

A

E = hf = Eb + ½mv2

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9
Q

Atomic Nucleus

A

A=Z+N

Z= Atomic No. (# of protons)

A= Mass No. (# of nucleons)

N = Neutron No.

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10
Q

Electron charge

A

1.602 × 10-19 Coulombs

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11
Q

Energy needed for a nucleus to disintegrate into individual nucleons

A

E = mc2

Einstein’s equation:

m = mass

c = speed of light

E = energy

Only mass can change…

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12
Q

Kinetic energy of accelerated ions

A

E = ½mv2 = qU

where:

U = potential difference

q = charge of ion

m = mass of the ion

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13
Q

Lamor’s frequency

A

ω = yB

w = lamor f. = MHz

y = gyromagnetic ratio [MHz / Tesla

B = strength of magnetic field [tesla]

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14
Q

Angular frequency

Lamor frequency of H atom?

A

ω = 2πf

for an H atom = 42.6 MHz

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15
Q

Equations for gyromagnetic ratios (inc. magnetic moment)

E = hf = ?

A

γ = gyromagnetic ratio [rad.s-1.T-1] - defined as ratio of magnetic moment μ [Am2] to its own angular momentum:

γ = μ / (ħ/2)

B = Strength of External Magnetic Field [T] = [N.m-1.A-1]

E = hf = 2μB

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16
Q

Ideal gas law

A

pV=nRT

p = pressure [Pa]

V = volume [m3]

n = number of moles [mol]

T = temp [K]

R = gas constant = 8.31 [J.K-1.mol-1]

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17
Q

Boltzmann’s constant and other way of writing ideal gas law

A

k = R/NA = 1.38 × 10-23 [JK-1]

NA = Avagadros constant = 6.022 × 1023 [mol-1]

pV = NkT

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18
Q

Boyles Law

A

P1V1 = P2V2

P = pressure V = volume

As pressure increases the volume decreases and vice versa

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19
Q

Charles Law

A

V1/T1 = V2/T2

V = volume T = temperature

As the temp increases, the volume increases and vice versa

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20
Q

Kinetic theory of gas

A

Average kinetic energy of one molecule of an ideal gas = (1/2)mc2 = (3/2)kT = (3/2)RT/NA

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21
Q

Law of Laplace

A

ΔP= T(1/R1+1/R2)

ΔP= T/R (for cylindrical form)

ΔP = 2T/R (for spherical form)

T= tension [N.m-1]

P= Pressure

R1/R2 = the radii of the membrane curvature at any given point.

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22
Q

Gibb’s phase rule

A

p+d = c+2

p = No. of phases

d = degree of freedom - d of heterogeneous system is number of independent variables (pressure, temp, conc); when p = 3 no variable can be changed as equilibrium would be lost, this is the triple point (no degree of freedom)

c = No. of components

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23
Q

Dalton’s law

A

p1+p2+p3+….+ = Pt

p1+p2+…+ = the pressure of mixture of gasses

Pt = the total pressure of the gasses.

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24
Q

Amagad’s law

A

v1+v2+v3+….+= Vt v1+v2+v3+…. += the volume of mixture of gasses. Vt = the total volume of the gasses

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25
Q

Relative humidity in analytical dispersion

A

φrel = φ / φmax

φ is the absolute humidity, so relative we divide it by the max and if we multiply it by 100 we get the % humidity.

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26
Q

Velocity of sedimentation

A

v = 2(ρ-ρ0)gr^2/9η V = velocity of sedimentation (שקיעה) ρ/ρ0 = density of the particle\liquid respectively r = radius of the particle η = viscosity coefficient g = gravity acceleration

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27
Q

Tangent tension

A

σ= F/S F= force of internal friction S= velocity gradient

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28
Q

Kinematic viscosity

A

ηk= η/ρ ρ= density η = dynamic viscosity

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29
Q

Viscosity of suspension

A

ηs = η(1+kc) η= viscosity of medium k = constant that characterizes the physical properties of the particle

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30
Q

Max velocity

A

Vmax= Δp*R^2/ 4ηL Δp = differences of pressure at both sides of the tube L= length of the tube R= radius.

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31
Q

Flow rate

A

Q= Δv/Δt

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32
Q

Flow rate of a tube with laminar flow and pressure differences

A

Q= πR^4ΔP/8ηL L = length of tube R = radius

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33
Q

Flow resistance

A

Rf = ΔP/Q

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34
Q

Measurement of viscosity

A

η/ηs= τρ/τs*ρs τ = time ρ/ρs = density of measured and standard liquid (respectively)

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35
Q

Stokes law (measurement of viscosity for a sphere)

A

F = 6πηrv F = internal friction force r =radius v = velocity η = viscosity

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36
Q

1st law of Fick

A

n/Aτ = -DΔc/Δx A = area through the diffusion takes place τ = time n = number of moles D = diffusion coefficient and it’s negative because the direction of the flux is opposite to the direction of the concentration gradient.

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37
Q

Diffusion coefficient

A

D = kT/6πηr k = boltzmann’s constant T = temperature r = radius η = medium viscosity

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38
Q

Gibb’s absorption equation

A

Γ = - c/RT* dσ/dc c= molar concentration R = universal gas constant dσ/dc = change of surface tension with respect to concentration T= temperature

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39
Q

Colligative properties

A

Φ = k*Cm Φ = k*Cg/M = Cm = Cg/M k = proportional constant Cm = concentration in molar M = molar mass Cg = g/liter Cm = kg/m^3

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40
Q

1st law of Raoult

A

Δp/p0 = n2/n1+n2 Δp = p0-p p0 = solvent Δp = change of pressure when a solution is added n1 = the number of particles of solvent

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41
Q

2nd law of Raoult

A

ΔTb,p = Ke*Cm ΔTb,p = Tb,p solution-solvent (boiling point) Ke = ebullioscopy constant (0.52 in water) Cm = concentration in molar

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42
Q

3d law of Raoult

A

ΔTf,p = Kc*Cm ΔTf,p = Tfp solution-solvent(freezing point) Kc = cryoscopy constant (1.86 in water) Cm = concentration in molar

43
Q

Van’t Hoff’s Law (osmotic pressure)

A

Posm = kCm Posm = RTCm Cm = concentration in molar R = gas constant T = temperature

44
Q

Starling’s equation of hydrostatic pressure

A

Jv = Kf ([Pc-Pi]-σ[πc-πi]) Jv = net fluid between compartments Kf = filtration coefficient (constant) Pc = Capillary hydrostatic pressure Pi = interstitial hydrostatic pressure πc = Capillary Osmotic pressure πi= interstitial osmotic pressure σ= reflection coefficient [Pc-Pi]-σ[πc-πi] = the net driving force

45
Q

Thermodynamic system

A

Isolated – Q= 0, W = 0, Σn = 0 Closed - Q ≠ 0, W = 0, Σn = 0 Open - Q≠0, W ≠ 0 , Σn ≠ 0 Q = heat (energy) W = work Σn = number of moles

46
Q

State equation, Gibb’s free energy equation

A

ΔG = ΔH – TΔS G = Free energy H = enthalpy S = entropy T= Temperature

47
Q

1st law of thermodynamics

A

ΔU= Uf-Ui = Q-W W+ is when the system performs work W- is when work is done on the system by its surroundings Q+ when heat enters the system Q- when heat flows out of the system Uf = final energy after addition Ui = initial energy

48
Q

2nd law of thermodynamics

A

Reversible isothermal processes – ΔS = 0 Irreversible processes - ΔS > 0 ΔS = entropy change

49
Q

Entropy (S) (j/k)

A

ΔS= Sf-Si= Qrev/T Qrev = amount of heat absorbed by a system

50
Q

Free Energy (F) (joules)

A

F = U-TS

51
Q

Free Enthalpy (G) (joules)

A

G = H-TS

52
Q

Chemical potential

A

μi = δG/δn Delta G = partial change in free enthalpy Delta n = partial change in number of moles

53
Q

Change of energy related to extensive\intensive factors

A

ΔE = μi* Δni μi = chemical potential (intensive factors) Δni = increase in number of moles (extensive factor)

54
Q

Work energy

A

W = Fd F = force d = displacement

55
Q

Isobaric

A

W = pΔv Only volume changes

56
Q

Isochoric

A

W = Q From 1st law of thermodynamics, since no work so only heat changes the internal energy

57
Q

Area of work done by\on the gas in adiabatic process

A

U= 3/2 nRT T = temp (K) R = gas constant (8.314) n = number of moles U = internal energy (J)

58
Q

Kelvin - Celsius relation

A

Tk=Tc+273

59
Q

Celsius – Fahrenheit relation

A

Tf = 9/5 Tc +32

60
Q

Liquid thermometers

A

ΔV = βVi*ΔT βVi = coefficient volumetric expansion ΔT = increase in temperature

61
Q

Calorimeter equation

A

Q = (M+K)cΔT M = mass of heated water in kg K = amount of water which requires some amount of heat to increase the temp by 1C as consumed by the device. C = specific heat ΔT = change of temp in heated water

62
Q

Specific Heat

A

Q = CMΔT Q = heat added C = specific heat M = mass ΔT = change in temp

63
Q

Latent heat

A

Q = mL Q = amount of energy released\absorbed during the change phase (in KJ) m = mass L = latent heat (in KJ/kg*m)

64
Q

Frequency of wave length

A

F = 1/T

65
Q

Acoustic amplitude

A

a = amax *sin(2πft)

66
Q

Wavelength

A

λ = c/f c = velocity f = frequency

67
Q

Acoustic velocity, effective velocity

A

c = √Χp/ρ (in gas medium) c = √k/ρ (in liquid) Vef = Vmax/√2=0.7*Vmax X = poisson’s constant p = pressure ρ = density k = elasticity

68
Q

Acoustic Pressure

A

P pmax*sin(2πft+π/2) Pef = Pmax/√2=0.7max Pef = Vef*cρ c = velocity of sound Vef = effective acoustic velocity ρ = density of medium

69
Q

Acoustic impedance (ratio of Pef to Vef)

A

Z = Pef/Vef = ρc (in pascal*s/m) Ratio between effective acoustic pressure to effective acoustic velocity.

70
Q

Doppler’s effect

A

λ = λ0 +- Vsource/f0(if observer is at rest) f = f0 (c+-vsource)/(c-+vdetector) (if movement of source and observer) Vsource = velocity of the source λ0 = c/f0, it’s the wavelength in case that the source is in rest. f0 = frequency +- depends if the source moves to or from the observer. vdetector = velocity of detector motion with respect to the medium. Vsource = velocity of source with respect to the medium. Upper sign is applied if the source and detector approach each other or not, lower sign is the opposite situation.

71
Q

Sound intensity

A

I = vef*Pef=Pef^2/ ρc

72
Q

Intensity level on log scale

A

L = 10log(I/I0) (in decibels) If I increases by 100, the intensity level (L) increases by 20 dB)

73
Q

Weber-Fechner’s law

A

ΔL = k*ΔI/I ΔI/I = stimulus ΔL = change in loudness

74
Q

Angle of incidence and angle of reflection (physical principles and diagnostic use of ultrasound)

A

sinθ1/sinθ2 = c1/c2 θ1 = angle of incidence θ2 = angle of reflection c1/c2 = velocities of corresponding medias

75
Q

Magnitude of electric and magnetic field

A

E= cB E = intensity of electric field B = intensity of magnetic field c = propagation of light.

76
Q

Propagation of light

A

c = 1/ √μ0*ε0 μ0= permeability constant of vacuum (4π*10^-7 H/m) ε0 = permittivity constant of vacuum (8.85*10^-12 F/m) c = 3*10^8 m/s

77
Q

Planck’s law (optics)

A

E = hf h = 6.62*10^-34(planck’s constant) and λ = c/F so => E = hc/λ

78
Q

Stefan – boltzmann’s equation

A

P/A = σT^4 P = power in watts A = surface area (m^2) Sigma = stefan Boltzmann constant (5.67*10^-8 w*m^2k^-4) T = temp in kelvin

79
Q

Wein’s law

A

λmax = a/T a = wein’s constant = 2.9*10^-3 mK

80
Q

Lens equation

A

1/f = 1/do + 1/di F = focal distance Do = object distance from lens Di = image distance from lens if: di >0 then image is on the right side if: di 0 – converging lens, f

81
Q

Optical power

A

D = 1/f - Units of optical power are diopter

82
Q

Magnification

A

M = - di/do=si/so Si = height of image So = height of object

83
Q

Extinction (absorbance) of light

A

I = Io*e^-ad I = intensity which has passed through the thickness Io = incident intensity d = medium thickness a = coefficient of absorption ( 10^-3*m^-1 is in air, glass is 1m^-1, metal is 10^6* m^-1)

84
Q

Absorption coefficient is proportional to concentration

A

A = ε’cm ln(Io/I) = ε’cmd E = εcmd = log Io/I (Lambert – Beer Law) this law is used in absorption photometry for measurements of concentrations. ε = molar extinction coefficient, its value depends on the type of molecules present in the solution, solvent and wavelength. Cm= concentration in molar Io = incident intensity I = intensity which has passed through the thickness Io = incident intensity d = medium thickness

85
Q

Rayleigh scattering

A

Is/Io = k*M^2/λ^4 Is = intensity of scattered light Io = incident intensity M = molar mass k = constant that depends on concentration of particles. Shorter wavelength = higher intensity

86
Q

Snell’s law

A

sin θ1/ sin θ2 = v1/v2 = n1/n2 n = c/v (v = c/n) (refractive index) ⇨ sinθ1/c/n2 = sinθ2/c/n1 ⇨ n2*sinθ2 = n1*sinθ1 θ1 = angle of incidence θ2 = angle of refraction v = velocity of the speed of light in respective medium n = refractive index of medium

87
Q

Constructive interference

A

Δδ = kλ k = 1,2,3,….. λ = wavelength Δδ = path difference

88
Q

Deconstructive interference

A

Δδ = (2k+1)*λ/2

89
Q

Relation between path difference and phase difference

A

Δφ = 2π/λ*Δδ Δφ = phase difference

90
Q

Path difference when a light passes through a thin layer of refractive index between 2parrallel lines

A

Δδ= 2d√(n^2-sin(α)^2) +λ/2 d = thickness of the layer α = angle of incidence

91
Q

Law of malus (polarization)

A

I = I0 *cos(α)^2 I0 = the intensity transmitted at alpha = 0 when the polarization axes are parallel and the same amount of light is transmitted through the 2nd polarizer and is transmitted through the first.

92
Q

Angle of Brewster

A

tg(θp) = n2/n1 θp = angle of Brewster we use this when reflected and refracted rays are perpendicular so from Snell’s law we get this formula

93
Q

Frequency of change from higher to lower state (Laser)

A

Vnm = En-Em/h En = higher state of energy Em = lower state of energy Vnm = Frequency

94
Q

Distance between 2 lenses (optical microscope)

A

d = Δ+fo+fe fo = focal length of objective lens fe = focal length of eyepiece lens(15mm) Δ = distance between the 2focal points of the lenses.

95
Q

Magnification of the 2 lenses (objective\eyepiece)

A

Mo = -Δ/fo Me = 0.25/fe Mtotal = - 0.25Δ/fo*fe

96
Q

Coulomb’s law

A

F = 1/4πε*(q1q2)/r^2 ε = permittivity F = repulsive or attractive force q1/q2 = 2charges between the force r = distance between the charges

97
Q

Relative permittivity

A

εrel = ε/ε0 ε= permittivity of an insulator ε0 = permittivity of vacuum (equals 8.85*10^-12)

98
Q

Intensity of an electric field

A

E = F/q0=1/4πε*q/r^2 Units in N/C

99
Q

Units in N/C E = F/q0=1/4πε*q/r^2

A

V = EPE/q0=(1/4πε0)*q/r [J/C]

100
Q

Internal potential (if solid phase of conductor in liquid phase)

A

φ = ψ+Χ φ = internal potential ψ = external potential Χ = value of the electric double layer

101
Q

Resistance- Ohm’s Law

A

R = V/I R = Resistance V = Voltage I = Current

102
Q

Resistance of a conductor

A

R = ρ*L/A ρ = material resistivity L = length of the resistor A = crossectional area

103
Q

Impedance (Z)

A

Z = U/I (Ohm’s law) Z = √R^2+(ωL-1/ωC)^2 Z = √R+Rc^2 (In tissues) Capacity resistance = 1/ωC Inductive resistance = ωL

104
Q

Kinetic energy of a particle

A

Ek = mv2 / 2 = p2 / 2m

Biophysics (10 decks)

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