BIOPHYSICS - BRIEF REVISION NOTES
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5. Types of radioactive decay
(alpha, beta, gamma, electron capture, nuclear fission, examples).
Alpha decay is when an atomic nucleus emits a alpha particle (2 protons and 2
neutrons) and transforms in to an atom with a mass number 4 less, and atomic
number 2 less.
Beta decay is when an electron or positron is emitted. In the case of an electron, it is
called B- decay, and for a positron it is called B+ decay.
Gamma Decay is when a high energy is emitted. This type of radiation has the
highest energy and frequency, and the shortest wavelength.
Electron Capture is when an electron is captured by a proton and is transformed in
to a neutron and neutrino.
Nuclear fission is the splitting of a heavy nucleus in to lighter parts, often producing
photons (in the form of gamma rays) and free neutrons as by products.
6. Law of radioactive decay
(explanation of the formulas, activity, Becquerel, Curie, half-life).
The law of radioactive decay is as follows:
-N / -t = N . y
Where N is the number of decayed nuclei over the short time t. N is the number of
nuclei existing at the beginning of the time period and y is a decay constant.
Nt = No . e
Where Nt is the number of nuclei at the time t, No is the number of nuclei capable of
decay at the start of the time, and e is the basis of natural logarithms.
Activity is the number of decays per second within the volume of the sample. Its
main unit is the Becquerel (Bq). 1 Becquerel is equal to one decay per second.
The older unit of activity is the Curie (Ci) which is the activity of one gram of radium.
1Ci = 3.7 x 1010 Bq
Physical half-life (Tp) is the time necessary for a drop in the activity of the
radioactive sample to a half of the initial value. Tp = In2/Yp where Yp is the decay
Biological half-life (Tb) is the time necessary for excreting half of the original
amount of any foreign substance from an organism.
7. Interaction of ionizing radiation with matter
(absorption, scattering, attenuation, attenuation coefficient, photoelectric effect,
Compton scattering, electron-positron pair production, interaction of alpha particles,
beta particles and neutrons).
Imagining a beam of radiation, some of the radiation particles disappear in various
ways (absorption) and some are deflected from their original direction of movement
Both these phenomenon reduce the intensity of the original beam, and are summed
up under the term attenuation.
I = Io . e-mx, where I is intensity of radiation, x/Io is intensity of incident radiation, e is
the basis of natural logarithms, u is the linear attenuation coefficient.
The attenuation coefficient depends on the type of radiation, the interacting
medium, and the density of the medium. The mass attenuation coefficient is u/p
where p is the density of the medium.
The photoelectric effect is when a photon is absorbed and an electron is emitted
from one of the shells of the electron. The energy of the incident photon is hf. The
work function is the energy needed to emit an electron.
hf= W + 1/2 mv2 where W is the work function.
During the photoelectric effect, the incident energy of the photon is converted to the
work function and kinetic energy of the electron.
Compton scattering is when a photon interacts with matter, and the electron emitted
doesn't absorb all the energy of the photon, so a new photon of lower energy is
originated. The change in the wavelength of the photon is called the Compton shift.
hf1 = W + hf2 + 1/2 mv2 where hf2 is the energy of the second photon.
Electron-positron pair production is when the energy of a photon is converted to
the mass and kinetic energy of an electron and a positron in the neighborhood of a
kinetic heavy atomic nucleus. The mass of the electron and positron are identical.
The minimum photon energy needed for pair production is 1.02 MeV.
The total linear attenuation coefficient is the sum of the linear attenuation
coefficients for the photoelectric effect, Compton scattering, and pair production.
U = t + o + pi
Interaction of radiation with matter occurs and has different results depending on
the type of radiation. Alpha radiation ionizes directly by impact, creating a large
number of ions. They lose energy very quickly and their path is short. Beta radiation
can ionize the medium. After ejection of one of the electrons the atom becomes
positively charged, and an accelerated electron can penetrate the nucleus to merge
with a proton and form a neutron. Neutrons ionize by indirect methods, both elastic
and inelastic impacts with the nucleus. Neutrons colliding with a heavy nucleus
rebound with almost no loss of energy, but light nuclei have great energy losses
which can be very dangerous in a biological environment.
8. Quantities and units used to quantify ionizing radiation
(whole chapter 2.1.4)
One electronvolt (eV) is the kinetic energy of an electron accelerated from rest state
by an electrostatic field, between two locations with a potential difference of 1V.
1eV = 1.602 x 10-19 J
The absorbed dose of a medium is expressed in Grays (Gy). It is defined as the
mean amount of energy deposited in a medium of a particular mass, divided by the
The dose rate is an expression of the absorbed dose related to the time expressed in
Photon ionizing radiation passing through air can be quantified by means of
exposure, given by the q/m ratio (C kg-1) where q is the charge generated in a small
volume of air with the mass m. Exposure rate is measured in C Kg-1 s-1.
9. Nature of chemical bonds
(molecular orbitals, covalent bond, ionic bond, dipole movement of chemical bond,
hydrogen bond, van der Wall forces)
Atoms with low number of electrons in the bonding orbitals have a tendancy to
donate electrons, and are called electropositive atoms. Those with high number of
electrons in the bonding orbitals have high affinity for electrons and are called
O bonds have overlapping in the join line of the nuclei of the atoms where the
highest density electrons are located.
bonds have overlapping elsewhere than the join line of the two nuclei.
Covalent bonds are based on the principle of sharing electrons between atoms. The
sharing can be even or uneven depending on the electronegativity of the atoms
Ionic bonds is when the shared electrons are solely bonded to one of the atoms
which becomes a negatively charged anion and the other atom in the bond becomes
Dipole movement is when a molecule has a distinguishable separate negative and
positive charge of magnitude +Q and -Q. The distance between the charges is called
vector, r. Dipole movement, u= Q.r (measured in C.m). One Debye (1D) is equal to
3.34 x 10-30 C.m.
Hydrogen bonding is when a hydrogen bonded to a highly electronegative atom
(N,O, or F) behaves as an electropositive element which is attracted to strong
negative atoms in other molecules.
Van Der Waals forces occur in permanent dipole-dipole interactions, dipole-induced
dipole interactions and dispersion interactions (between induced dipoles).
10. Viscosity of Liquids
(Newton's law of viscous flow, Newtonian and non-Newtonian liquids, how to
Viscosity is the measure of internal friction in a liquid. Viscosity is independent of
pressure except at very high pressure. Viscosity falls as temperature increases.
When a liquid flows the layers move at different velocities, and the viscosity arises
from the shear stress between the layers. Newton stated that for straight parallel and
uniform flow, the shear stress T between layers is proportional to the velocity gradient
du/dy, in the direction perpendicular to the layers. T=n du/dy, where n is the
coefficent of viscosity.
Newtonian liquids, such as water, obey this law. Non-Newtonian liquids cannot be
described by a single number for viscosity.
Measuring of viscosity can be done using an Oswald Viscometer which has a
capillary arm and two gauge marks. A known amount of liquid can be pipetted in to
the capillary arm sucked by a rubbed tube to make the level of liquid rise above the
upper gauge mark. The time taken for it to flow from the upper to lower gauge marks
is measured, and it is possible to measure the kinematic viscosity (V) using the
V = t/to . vo where t is time, to is time of reference liquid and vo is kinetic viscosity of
the reference liquid.
16. Types of dispersion systems and their properties
colloids and their physical properties, gel-sol, macroheterogeneous systems,
If two types of particles, or two different physical phases, which are intermingled,
occur in a system it is called a dispersion system. We can distinguish them in to a
dispersion medium and a dispersed phase. Depending on the dispersed phase,
dispersions can be classified as true solutions, colloids and macroheterogeneous
systems. Macroheterogeneous systems can be seen by light microscopes, but
colloids can only be seen by transmission electron microscopes.
Properties of colloid systems; they are produced by two methods. Dispergation
consists of dissolving larger particles, producing molecular colloids. If the particles
disperse easily with no tendency to re-aggregate, it is referred to as lyophilic. If the
colloid solution doesn't form easily it is called lyophobic. The creation of a salvation
envelope and the electric charge on colloid particles enable the particles in the
solution to stay dispersed. Liquid colloids are called sol, and solid colloids are called
gel, formed by gelatinization.
The ion cloud can be divided in to an internal and external part. The internal part is
stable and the external part is less ordered. This distribution of charge on the colloid
particle is the reason for the arising electric potential. The potential difference
between the stable and diffusive part of the ion cloud is described as electrokinetic
potential and the value does not exceed 100mV. It determines the behavior of colloid
particles in electric field and their electrostatic repulsion.
17. Centrifuges, sedimentation analysis and electrophoresis
forces taking part in sedimentation, sedimentation coefficient, forces acting on a
charged particle in an electric field, electrophoretic mobility, safety aspects of
The centrifuge uses the sedimentation principle, where centripetal acceleration is
used to separate substances of greater and lesser density. Low speed centrifuges
are used to accelerate the sedimentation of bigger particles e.g. cells. High speed
centrifuges serve for the separation of biomacromolecules.
Three forces affect sedimentation;
Buoyant force, F=pVa=pVrw2
p = particle density
V = particle volume
A = centrifugal acceleration
r = radius of rotation
w = angular velocity
Centrifugal force, F=mrw2
M = mass
Frictional force, stokes formula, F=6prhv
R = radius of particle
H = dynamic velocity
V = velocity of particle moving in the liquid
Sedimentation coefficient s = v _ w2 r
Electrophoresis is the movement of charged molecules in an electrical field. Friction
force is given by stokes formula, F=6prhv. The electric field acts by the force F=zeE
where z is the number of elementary charges, e is the elementary charge and E is
the intensity of the electric field.
Safety aspects. Main errors are failure to place lid on rotor securely, overloading the
rotors maximum mass, running rotor with missing buckets, and buckets hooked
incorrectly so that they can't swing properly. The following procedures are
Examine tubes and bottles for cracks or stress marks
Wipe outside of tubes before using
Never overfill more than 3 quarters of the tube
Always use screw cap before spinning
Never exceed safe rotor speed
Ensure that the load is balanced
Stop the centrifuge immediately incase of an unusual condition
18. Basic concepts of the law of thermodynamics
Thermodynamic systems, equilibrium, reversible and irreversible process, work of
thermodynamic system, explanation of difference between temperature and heat
Every set of particles influencing one another can be considered a thermodynamic
system. An isolated system doesn't exchange matter or energy with its surroundings,
a closed system only exchanges energy, and an open system exchanges both mass
If a system passes through a sequence of equilibrium states, it is a reversible
process. If a system passes through a sequence of non-equilibrium states it is an
A thermodynamic system can do work;
Gas and piston system; W= pressure x change of volume
W = Q . U is the work necessary to transfer a charge Q between places with potential
difference of U.
Chemical system; W = chemical potential, m X change in number of moles, n
Temperature is a measure of the thermal state of matter.
Heat, or thermal energy, is the part of internal energy of a system which can be
exchanged between systems as a result of their different temperatures.
19. Equations of state and basic thermodynamic processes
Universal gas law, van der Waals equation, isothermal, isobaric, isochoric and
Universal gas law is pV=nRT
Van der Waals real gas law is xxx
An isothermal process is one where the temperature is constant, expressed by
boyles law; p.V= constant
An isobaric process is one where the pressure is constant, expressed by the Gay
Lussacs Law; V_T = constant
An isochloric process is one in which the volume is constant, expressed by mayers
equation; P_T = constant
An adiabatic process is one where the entropy is constant, expressed by the
poissons equation; pV sq.rt k = constant
20. First and Second law of thermodynamics
Including meaning of entropy, thermodynamic potentials - enthalpy, free energy, free
entropy, chemical potential, chemical equilibrium and chemical work
First Law is the conservation of energy. Change in U = W + Q. Energy cannot be
created or destroyed, just converted in to other forms.
Second Law determines the direction of a process, using entropy. Change in S =
Q_T where Q is the amount of heat added to the system at temperature T.
Enthalpy is an additive state variable given by the formula H= U + p.V
Free energy is an additive state variable given by the formula F= U - T.s
Free enthalpy is an additive state variable given by the formula G = H - T.S
If enthalpy decreases = exergonic reaction.
If enthalpy increases = endergonic reaction.
21. How to explain that entropy is a measure of system ordering
Entropy can be defined according to three different perspectives; macroscopic,
microscopic and information theory.
Entropy depends on the number of possible microscopic arrangements that result in
the same observed macroscopic arrangements of a thermodynamic system.
Boltzmanns formula relates this formula;
S = k. In W
W = number of microscopic arrangements
K = boltzmann constant =1.38 x 10-23
S = state parameter
Microstate= position or arrangement of particles within a thermodynamic system
Macrostate= observable and measurable state of thermodynamic system
22. Osmotic Pressure
(explain its origin, van't Hoff's formula, osmolarity, tonicity)
Osmotic pressure belongs to the colligative properties (depends on the number of
particles) of thermodynamic systems.
A system can reach thermodynamic equilibrium by equalizing concentrations of
substances throughout the whole volume of the system. Osmotic pressure is the
exact amount of pressure needed to oppose and stop osmosis.
Van't Hoff's Formula: pi = icRT
Pi = osmotic pressure - Pa
C = solute concentration
R = universal gas constant 8.314
T = absolute temperature
Osmolarity = ic
Tonicity is the measure of effective osmolarity, and is a property of a solution in
reference to a particular membrane. Solutions with lower osmotic pressure are
hypotonic, with higher are hypertonic, with equal are isotonic.
23. Phases and phase equilibrium
(Gibb's phase rule, Raoult's Law, Henry's Law, Ebullioscopy, and Cyroscopy)
There are three phases of mater: solid, liquid and gas. Gibb's phase rule is important
to understand transitions between phases.
V = K - f+2
The number of degrees of freedom (v) of the system is the number of intensive
state variables, which can be independently modified, without changing the number
of phases in the system.
K is the number of components. F is the number of phases.
Raoult's Law pA = p*A . xA
xA = concentration of component A
p*A = pressure of the saturated vapour
The partial pressure of the saturated vapour of the component (solvent) over the
solution is equal to the pressure over the pure component
Henry's Law pP = k . Xp
pP is the partial pressure of the dissolved gas
k is a constant
Xp is the mole fraction of the dissolved gas
At a given temperature, the amount of gas dissolved in the liquid is proportional to
the partial pressure of the gas above the liquid.
Ebullioscopy and cryoscopy are colligative properties of solutions.
The presence of solute raises the boiling point = ebillioscopy.
The presence of solute lowers the melting point = cryoscopy.
24. Surface tension
(Definition, Laplace equation, gibb's absorption equation, surfactants and their
biophysical importance, how to measure surface tension)
Surface tension, o, is defined as the force F acting in parallel with the surface of the
of the liquid perpendicular to length unit, l.
It is strongly dependant on temperature, it rises with temperature.
p = 2o/r
where p is pressure difference inside and
outside the liquid, and r is the radius of the liquid surface curvature.
Gibbs Absorption law xxx
Surfactants and their biophysical importance:
Pulmonary surfactant decreases surface tension, insufficiency can lead to pulmonary
Proteins undergo a conformational change in a phase interface.
Salts of bile acids are used to disperse drops of fat in water as emulsifying agents.
33. Blood flow
(equation of continuity, Bernoulli's equation, Hagen-Poiseuille Law, Reynolds number
and critical velocity, elastic and muscular vessels, resistance of the vessel bed, how
to measure blood flow, oncotic pressure and it's importance for capillary filtration.
40. Electrical excitability of tissues
(I/t curve, reobase, chronaxy, clinical importance)
Electrical excitability of tissues is the ability of them to respond to an electrical
stimulus. It's a property found more often in nervous and muscular tissues.
Rheobase: threshold intensity
Chronaxy: period of time necessary to evoke excitation at a current intensity
Chronaxy is equal to twice the value of the rheobase. It is derived from the I/t curve,
which is intensity of an electrical current versus it's duration. It can be divided in to
AC and DC which have important clinical uses.
Direct Current: increase local metabolism, accelerate the diffusion, increase
perfusion and accelerate the resorption of inflammations which relieves pain.
Alternating Current: Defibrillator, Cardiostimulator, Electrostimulation of nerves and
muscles, Electrostimulated breathing, and Electroconvulsive therapy.
41. Sensory Receptors
(types of receptors, receptor cells and their common features, receptor potential,
Weber-Fechner law, adaptation)
Types of receptors: mechanoreceptors, thermoreceptors, chemoreceptors, and
photoreceptors. Each receptor responds to a specific type of stimulus modality called
adequate stimulus to which the receptor is most sensitive. They convert a stimulus in
to an electric signal.
Telereceptors are capable of detecting stimuli from a remote source.
Exteroreceptors respond to stimuli from being directly in touch.
Proprioreceptors are located in muscles, tendons and joints.
Interoreceptors are situated in internal organs.
Ir = k1.log Is
Ir = intensity of stimulus
Is = intensity of impulse