Situational problems
1. Calculate permittivity of membrane lipids if membrane thickness is d=10 nm, specific capacitance is С=1,7 2. What distance does phospholipid molecule pass in 1 second on the surface of red blood cell membrane as a result of lateral diffusion? Coefficient of lateral diffusion is 10–12 m2/s. Compare with red blood cell circumference with 8 µm diameter. 3. At phasic transition of membrane phospholipids from liquid-crystal state to gel the thickness of bilayer changes. How will the electric capacity of membrane change? How will the strength of electric field in membrane change? 4. How will the electrical (specific) capacity of membrane change at its transition from liquid-crystal state to the gel if it is known that in liquid-crystal state the thickness of hydrophobic layer is 3,9 nm and in the state of gel it is 4,7 nm. Permittivity of lipids» 2. 5. Calculate the time 6. Calculate the permeability coefficient for a substance which flow through the membrane is 5∙10-5 mol/m2∙s. Substance concentration inside the cell is 7. How many times intracellular concentration of potassium ions has to exceed the outside concentration in order to establish 91 mV resting potential? Calculate the cell temperature. 8. Calculate the distribution coefficient K for a substance if membrane thickness is 10 nm, diffusion coefficient is 7,2∙10-8 cm2/s, permeability coefficient is 14 cm/s. 9. Molecule concentration difference on the membrane of a cell is 48 mmol/L, coefficient of distribution between membrane and environment is 30, diffusion coefficient is 1,5∙10-12 m2/s, flow density is 25 mol/m2∙s. Calculate the thickness of this membrane. 10. Find the permeability coefficient for formamide of Mycoplasma plasmatic membrane if concentration difference of this substance inside and outside the membrane is 0,5∙10-4 M, its flow density through the membrane is 8∙10-4 M∙cm/s. 12. Calculate the energy that is necessary for completeing of one cycle by Na+, K+ - АТP-ase in giant axon of squid if transmembrane potential of this cell is 60 mV, concentrations of potassium and sodium ions inside and outside the cell are 13. How many times concentration of small cations has to exceed the concentration of macromolecules in order to have Donnan potential difference -2 mV at 200С temperature? Average charge of macromolecules is z=−15. 14. How many times outside concentration с0 of sodium ions has to exceed the inside concentration сj in order to establish +50 mV equilibrium Nernst potential Δφ at 270С temperature? 15. Specific electric capacitance of axon membrane measured by intracellular microelectrode is 0,5 µF/cm2. Using the formula of plane capacitor evaluate the thickness of hydrophobic layer of membrane with permittivity e» 2. 16. What distance does phospholipid molecule pass in 1 second on the surface of red blood cell membrane as a result of lateral diffusion? Coefficient of lateral diffusion is 10–12 m2/s. Compare with red blood cell circumference with 8 µm diameter. 17. Critical radius of lipid pore in the membrane depends on edge tension γ, surface tension of the membrane s and membrane potential j. Deduce a formula for the critical radius of a pore. Calculate the critical radius of a pore at the absence of membrane potential. Edge tension of the pore is 10-11 N, surface tension of lipid bilayer is 0,3 mN/m. 18. At phasic transition of membrane phospholipids from liquid-crystal state to gel the thickness of bilayer changes. How will the electric capacity of membrane change? How will the strength of electric field in membrane change? 19. At phasic transition of membrane phospholipids from liquid-crystal state to gel the thickness of bilayer changes. How will the electric capacity of membrane change? How will the strength of electric field in membrane change? 20. How will the electrical (specific) capacity of membrane change at its transition from liquid-crystal state to the gel if it is known that in liquid-crystal state the thickness of hydrophobic layer is 3,9 nm and in the state of gel it is 4,7 nm. Permittivity of lipids» 2. 21. Osmotic pressure of human blood is 0,77 MPa. How many moles of NaCl salt has to contain isotonic physiological solution in 200 ml of water at at 370С temperature? 22. At the repeated registering of NMR spectrum of the same sample the temperature has changed and spectrum lines have become narrower. Has the temperature decreased or increased? 23. Find the electromagnetic wavelength at which the electron paramagnetic resonance (EPR) arises in magnetic field with magnetic induction 0,3 T. Landé g-factor is two. 24. Current flows through the contour with 0,5 m radius. Find the current if it is known that magnetic moment of the contour is p=10 µB. 25. At what angle γ is electrical vector of heart to lead axis located at this moment of time if potential difference Δφ=0,68 mV was fixed and maximal potential difference in this lead is Δφmax=0,80 mV? 26. Determine the power of heat radiation of undressed person with S=1 m2 area of body surface; skin temperature is t1=300C, environment temperature is t2=200C. Absorption coefficient of skin is k=0,9. 27. Intensiveness of human body radiation has increased for 2,62%. By what percentage has the temperature increased? 28. Determine the wavelength λmax, corresponding to the maximum of spectral density of human body irradiance considering it as grey body. Skin temperature is t=30 0C. 29. Determine the molar absorption coefficient of substances ε if at its concentration in a solution С=0,03 mol/L optical density of the solution is D=1. Cuvette length is l=2 cm. 30. Observing the movement of red blood cells in a capillary velocity of blood flow can be measured (υcp=0,5 mm/s). Average velocity of blood flow in aorta is υf=40 cm/s. Using these data determine how many times the sum of all functioning capillaries is more that the section of aorta. 31. Determine the electronic microscope resolution limit z if accelerating voltage in it is U=100 kV, aperture angle is u=10-2 rad. 32. Calculate the blood viscosity η at normal hematocrit (с=45%) if the plasma viscosity is η0=2,0 mPa∙s. 33. Calculate the maximal minute volume Qmax of blood at which blood flow in aorta stays laminar. Diameter of aorta is d=2 cm, blood viscosity is η=5 mPa∙s, density is ρ=1050 kg/m3. Critical value of Reynolds number is Reкр=2000. 34. Velocity of pulse wave propagation in artery is υ=10 m/s. Determine the elastic modulus of artery E if the thickness of its wall is h=0,7 mm, internal diameter is d=8 mm, blood density is ρ=1050 kg/m3. 35. Radius of aorta is 1,0 cm; velocity of blood flow in aorta is 30cm/s. What is the velocity of blood flow in capillaries if the summary sectional area of capillaries is 2000 cm2. (Diameter of one capillary is 8∙10-4 cm and amount of capillaries is more than million). 36. In medicine for determination the movement velocity of separate biological structures (for example, blood, heart valves) Doppler effect is used. How is the changing of ultrasound signal frequency connected with its velocity at reflection from moving subject? 37. To the piston of horizontally placed syringe F=10 N force is applied. Determine the velocity υ of medicine flowing out from the syringe needle if density of the medicine is ρ=1050 kg/m3, piston diameter is d=7 mm, at that its area is much more greater than the cross-sectional area of the needle. 38. What is the velocity υ of air bubble bobbing up with diameter d=4 mm in a vessel filled with glycerol? Kinematic viscosity of glycerol is ν=1,17∙10-3 m2/s, its density is much more greater than air density. 39. At some diseases critical Reynolds number in vessels becomes 1160. Find the blood flow velocity at which transition of laminar flow to turbulent one is possible in a vessel with diameter 2 mm. 40.The level of loudness is 120 phon and the level of quiet talking in the same distance is 41 phon. Determine the ratio of intensities. 41. Sound intensity is 10-2 W/m2. Find the sound pressure if the acoustic resistance of the medium (air) is 420 kg/m2s. 43. Determine the amplitude value of sound pressure for the clear tone with 1000 Hz frequency at which the rupture of the eardrum can happen if it happens at the loudness level LE=160 phon. (The answer has to be in Pa and atm.). 44. Electroheater in the apparatus for heat treatment of medicinal raw in 10 minutes vaporizes 1 L of water taken at the temperature 200С. Determine the length of nichrome wire with 0,5 mm2 section considering that the apparatus is powered with 120 V voltage and its energy conversion efficiency is 80%. 45. Intensiveness of the light passed through the aspirin solution in non-absorbing solvent decreases due to absorption in three times. Concentration of aspirin molecules is n0=1020 m-3. Way of the light in solution is l=150 mm. Determine the effective section σa of aspirin absorption. 46. Determine the difference of phases Δφ in pulse wave between two points of an artery located in distance Δx=20 cm from each other considering the velocity of pulse wave is υ=10 m/s, heart oscillations are harmonic with frequency ν=1,2 Hz. 47. Fragments of molecules 48. In one of the leads the greatest biopotentials difference on electrocardiogram is 2 mV. Assuming that electric moment of heart is parallel to the Einthoven triangle from which electrocardiogram is taken assess the value of heart electric moment. It is known 49. For the heating of muscular tissue voltage U=U0sinwt with amplitude U0=250 V and frequency ν=106 Hz is applied on plane electrodes. Active resistance of this part of the circuit is R=103 Ω; capacitance is С= 50. Ionophoresis is used for introduction of medicinal substances into the human body. Determine the amount of once ionized ions of the medicinal substance introduced to a patient in time t=10 min at the current density j=0,05 mA/cm2 from the electrode with area S=5 сm2.
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of sedentary life and the frequency of hoppings 
from one membrane layer to another one of the lipids of sarcoplasmic reticulum membrane if the coefficient of lateral diffusion is D=12 µm2/sec and the area of one phospholipid molecule is А=0,7 nm2.
, outside - 
mol/L.
mmol/L and 
mmol/L, 
mmol/L and 
mmol/L respectively. Cell temperature is 370С.
and СH3+ accelerated with the same potential difference fly into the homogeneous magnetic field at an angle π/2 towards its direction. Determine the ratio of trajectories radii of these particles.
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F. Determine the heat released in volume of the tissue between electrodes during the oscillations period T and during the time of procedure t=10 min.
