Biophysics Formulae Flashcards
De broglie’s equation (wave)
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
Energy of a photon relating to frequency
E = hf = h(c/λ)
Max number of electron in a shell (n)
2n2
Max number of electron in a subshell (s)
4l+2
Magnetic quantum number
2l+1
Spin quantum number
+- 1/2
Ionization
Eb = -E
Ionization: Einstein’s equation for photoelectric effect
E = hf = Eb + ½mv2
Atomic Nucleus
A=Z+N
Z= Atomic No. (# of protons)
A= Mass No. (# of nucleons)
N = Neutron No.
Electron charge
1.602 × 10-19 Coulombs
Energy needed for a nucleus to disintegrate into individual nucleons
E = mc2
Einstein’s equation:
m = mass
c = speed of light
E = energy
Only mass can change…
Kinetic energy of accelerated ions
E = ½mv2 = qU
where:
U = potential difference
q = charge of ion
m = mass of the ion
Lamor’s frequency
ω = yB
w = lamor f. = MHz
y = gyromagnetic ratio [MHz / Tesla
B = strength of magnetic field [tesla]
Angular frequency
Lamor frequency of H atom?
ω = 2πf
for an H atom = 42.6 MHz
Equations for gyromagnetic ratios (inc. magnetic moment)
E = hf = ?
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
Ideal gas law
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]
Boltzmann’s constant and other way of writing ideal gas law
k = R/NA = 1.38 × 10-23 [JK-1]
NA = Avagadros constant = 6.022 × 1023 [mol-1]
pV = NkT
Boyles Law
P1V1 = P2V2
P = pressure V = volume
As pressure increases the volume decreases and vice versa
Charles Law
V1/T1 = V2/T2
V = volume T = temperature
As the temp increases, the volume increases and vice versa
Kinetic theory of gas
Average kinetic energy of one molecule of an ideal gas = (1/2)mc2 = (3/2)kT = (3/2)RT/NA
Law of Laplace
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.
Gibb’s phase rule
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
Dalton’s law
p1+p2+p3+….+ = Pt
p1+p2+…+ = the pressure of mixture of gasses
Pt = the total pressure of the gasses.
Amagad’s law
v1+v2+v3+….+= Vt v1+v2+v3+…. += the volume of mixture of gasses. Vt = the total volume of the gasses
Relative humidity in analytical dispersion
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.
Velocity of sedimentation
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
Tangent tension
σ= F/S F= force of internal friction S= velocity gradient
Kinematic viscosity
ηk= η/ρ ρ= density η = dynamic viscosity
Viscosity of suspension
ηs = η(1+kc) η= viscosity of medium k = constant that characterizes the physical properties of the particle
Max velocity
Vmax= Δp*R^2/ 4ηL Δp = differences of pressure at both sides of the tube L= length of the tube R= radius.
Flow rate
Q= Δv/Δt
Flow rate of a tube with laminar flow and pressure differences
Q= πR^4ΔP/8ηL L = length of tube R = radius
Flow resistance
Rf = ΔP/Q
Measurement of viscosity
η/ηs= τρ/τs*ρs τ = time ρ/ρs = density of measured and standard liquid (respectively)
Stokes law (measurement of viscosity for a sphere)
F = 6πηrv F = internal friction force r =radius v = velocity η = viscosity
1st law of Fick
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.
Diffusion coefficient
D = kT/6πηr k = boltzmann’s constant T = temperature r = radius η = medium viscosity
Gibb’s absorption equation
Γ = - c/RT* dσ/dc c= molar concentration R = universal gas constant dσ/dc = change of surface tension with respect to concentration T= temperature
Colligative properties
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
1st law of Raoult
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
2nd law of Raoult
ΔTb,p = Ke*Cm ΔTb,p = Tb,p solution-solvent (boiling point) Ke = ebullioscopy constant (0.52 in water) Cm = concentration in molar
3d law of Raoult
ΔTf,p = Kc*Cm ΔTf,p = Tfp solution-solvent(freezing point) Kc = cryoscopy constant (1.86 in water) Cm = concentration in molar
Van’t Hoff’s Law (osmotic pressure)
Posm = kCm Posm = RTCm Cm = concentration in molar R = gas constant T = temperature
Starling’s equation of hydrostatic pressure
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
Thermodynamic system
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
State equation, Gibb’s free energy equation
ΔG = ΔH – TΔS G = Free energy H = enthalpy S = entropy T= Temperature
1st law of thermodynamics
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
2nd law of thermodynamics
Reversible isothermal processes – ΔS = 0 Irreversible processes - ΔS > 0 ΔS = entropy change
Entropy (S) (j/k)
ΔS= Sf-Si= Qrev/T Qrev = amount of heat absorbed by a system
Free Energy (F) (joules)
F = U-TS
Free Enthalpy (G) (joules)
G = H-TS
Chemical potential
μi = δG/δn Delta G = partial change in free enthalpy Delta n = partial change in number of moles
Change of energy related to extensive\intensive factors
ΔE = μi* Δni μi = chemical potential (intensive factors) Δni = increase in number of moles (extensive factor)
Work energy
W = Fd F = force d = displacement
Isobaric
W = pΔv Only volume changes
Isochoric
W = Q From 1st law of thermodynamics, since no work so only heat changes the internal energy
Area of work done by\on the gas in adiabatic process
U= 3/2 nRT T = temp (K) R = gas constant (8.314) n = number of moles U = internal energy (J)
Kelvin - Celsius relation
Tk=Tc+273
Celsius – Fahrenheit relation
Tf = 9/5 Tc +32
Liquid thermometers
ΔV = βVi*ΔT βVi = coefficient volumetric expansion ΔT = increase in temperature
Calorimeter equation
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
Specific Heat
Q = CMΔT Q = heat added C = specific heat M = mass ΔT = change in temp
Latent heat
Q = mL Q = amount of energy released\absorbed during the change phase (in KJ) m = mass L = latent heat (in KJ/kg*m)
Frequency of wave length
F = 1/T
Acoustic amplitude
a = amax *sin(2πft)
Wavelength
λ = c/f c = velocity f = frequency
Acoustic velocity, effective velocity
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
Acoustic Pressure
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
Acoustic impedance (ratio of Pef to Vef)
Z = Pef/Vef = ρc (in pascal*s/m) Ratio between effective acoustic pressure to effective acoustic velocity.
Doppler’s effect
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.
Sound intensity
I = vef*Pef=Pef^2/ ρc
Intensity level on log scale
L = 10log(I/I0) (in decibels) If I increases by 100, the intensity level (L) increases by 20 dB)
Weber-Fechner’s law
ΔL = k*ΔI/I ΔI/I = stimulus ΔL = change in loudness
Angle of incidence and angle of reflection (physical principles and diagnostic use of ultrasound)
sinθ1/sinθ2 = c1/c2 θ1 = angle of incidence θ2 = angle of reflection c1/c2 = velocities of corresponding medias
Magnitude of electric and magnetic field
E= cB E = intensity of electric field B = intensity of magnetic field c = propagation of light.
Propagation of light
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
Planck’s law (optics)
E = hf h = 6.62*10^-34(planck’s constant) and λ = c/F so => E = hc/λ
Stefan – boltzmann’s equation
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
Wein’s law
λmax = a/T a = wein’s constant = 2.9*10^-3 mK
Lens equation
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
Optical power
D = 1/f - Units of optical power are diopter
Magnification
M = - di/do=si/so Si = height of image So = height of object
Extinction (absorbance) of light
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)
Absorption coefficient is proportional to concentration
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
Rayleigh scattering
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
Snell’s law
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
Constructive interference
Δδ = kλ k = 1,2,3,….. λ = wavelength Δδ = path difference
Deconstructive interference
Δδ = (2k+1)*λ/2
Relation between path difference and phase difference
Δφ = 2π/λ*Δδ Δφ = phase difference
Path difference when a light passes through a thin layer of refractive index between 2parrallel lines
Δδ= 2d√(n^2-sin(α)^2) +λ/2 d = thickness of the layer α = angle of incidence
Law of malus (polarization)
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.
Angle of Brewster
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
Frequency of change from higher to lower state (Laser)
Vnm = En-Em/h En = higher state of energy Em = lower state of energy Vnm = Frequency
Distance between 2 lenses (optical microscope)
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.
Magnification of the 2 lenses (objective\eyepiece)
Mo = -Δ/fo Me = 0.25/fe Mtotal = - 0.25Δ/fo*fe
Coulomb’s law
F = 1/4πε*(q1q2)/r^2 ε = permittivity F = repulsive or attractive force q1/q2 = 2charges between the force r = distance between the charges
Relative permittivity
εrel = ε/ε0 ε= permittivity of an insulator ε0 = permittivity of vacuum (equals 8.85*10^-12)
Intensity of an electric field
E = F/q0=1/4πε*q/r^2 Units in N/C
Units in N/C E = F/q0=1/4πε*q/r^2
V = EPE/q0=(1/4πε0)*q/r [J/C]
Internal potential (if solid phase of conductor in liquid phase)
φ = ψ+Χ φ = internal potential ψ = external potential Χ = value of the electric double layer
Resistance- Ohm’s Law
R = V/I R = Resistance V = Voltage I = Current
Resistance of a conductor
R = ρ*L/A ρ = material resistivity L = length of the resistor A = crossectional area
Impedance (Z)
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
Kinetic energy of a particle
Ek = mv2 / 2 = p2 / 2m
