New Minimum Requirement Questions for Biophysics
A great way to learn the key concepts in biophysics!!...
Contents 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Basic physical definitions ............................................ ............................................1 1 Atomic physics, electromagnetic waves, X‐ray ........... 2 Absorption, luminescence, lasers ............................... 3 Geometrical optics, microscopy, electron microscopy 4 Nuclear physics, radioactivity...................................... radioactivity ......................................5 5 Interaction of radiation with material, detection of radiation ...................................................................... ......................................................................6 6 Radiation biophysics, dosimetry, biological effect of radiations .................................................................... ....................................................................6 6 Experimental and diagnostic use of isotopes, accelerators, gamma camera CT, PET, SPECT.............. 7 Basic principles and applications of nuclear magnetic resonance (NMR). Electrospin resonance. .................. 7 Thermodynamics......................................................... Thermodynamics.........................................................9 9 Diffusion...................................................................... Diffusion ......................................................................9 9 Biological membranes and membrane transport ..... 10 Biophysics of the of the Sensory System ............................. 12 Sound, Ultrasound .................................................... ....................................................13 13 Information and entropy, communication systems, feedback.................................................................... feedback ....................................................................13 13 Modern microscopies, flow cytometry, sedimentation, electrophoresis (Medicine students only)................. only) ................. 14
Basic physical definitions
Define kinetic energy in words and with a formula, and give its unit! Kinetic energy is the amount of work an object with a mass of m moving at a speed of v can can perform while its speed is reduced to zero: 1 2 Ekinetic mv 2 The unit of kinetic energy is joule.
Define electron volt (eV)! Electron volt is a unit of energy. It is equivalent to the amount of kinetic energy gained by a single electron when accelerated through a voltage difference of 1 V.
Define what force is! Force is a vector quantity characterizing the capability to cause acceleration.
Define moment moment of inertia inertia in words words and with a formula! Moment of inertia (I ) serves the same purpose in circular motion as mass in linear motion. It characterized the resistance of an object against angular acceleration, i.e. the change in angular velocity. Moment of inertia of a point-like object can be calculated by the following equation: I mr 2 , where m is the mass of the object, r is the distance of the object from the axis of rotation.
Define angular momentum! Angular momentum is analogous to momentum, it serves the same purpose in circular motion as momentum does in linear motion. By definition, the product of the angular velocity and the moment of inertia of an object is its angular momentum.
Define the potential energy of of an object in a homogenous gravitational field! The potential energy of an object with mass m at a height of h in a homogenous gravitational field characterized by a gravitational acceleration of g is given by the following equation:
Define the potential energy energy of a charged object in an electrostatic field! The electrostatic potential energy of an object with charge Q at position A in an electrostatic field is: E pot QU A ,where U A is the electric potential at point A.
Define work work in words and with a formula! Work is the amount of energy transferred by a force. It can be calculated according to the follo wing formula: W Fs , where W is work, F is force and s is the displacement of the object in the direction of the force.
Formulate the general form of of the work-energy work-energy theorem, and its special form for the electric and homogenous gravitational fields!
Define momentum in words and with a formula! Momentum (p) is the product of the mass (m) and the velocity (v) of an object:
Define acceleration in words and with a formula! Acceleration is the rate of velocity velocity change with time: dv , where a is acceleration, dv is the change in dt velocity in time t .
Define angular velocity in words words and and with with a formula! Angular velocity ( ) is the ratio of the angle ( , usually measured in radians) traversed to the amount of time (t ) it takes to traverse the angle:
Define Newton’s 2nd law in words and with a formula! The acceleration of an object (a) is given by the ratio of the net (or resultant) force acting upon it (Fn) and the mass of the object (m): F a n m
, m is the mass, v B and v A are the speed of the object at point A and B, respectively, W AB is the work done on the object between points A and B. In an electric field: Ekinetic, B E kinetic, A QU AB , Q is the
Define centripetal acceleration in words and with a formula! Centripetal acceleration (ac ) is the rate of change in the direction of velocity with time:
charge of the object, U AB is electric potential difference between points A and B In a homogenous gravitational field: h , is the height difference Ekinetic , B Ekinetic, A mghAB AB
is velocity, r is is the radius of the 2 r , where v is
General form: E kinetic , B
E kinetic, A
between points A and B.
r path, is is angular velocity.
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m v 2B v 2A
Define power in words and with a formula, and give its unit! Power is the rate at which work is done, and it is calculated according to the following formula: P W , t where P is power, W is the amount of work perform in
time t . The unit of power is watt (W 16.
What is the wavelength range of ultraviolet radiation? 10nm – 400nm 24.
What is the wavelength range of infrared radiation? 750nm – 1mm
Define the limiting frequency (f max ) of braking radiation at an accelerating voltage of U. eU f max h where h is Planck's constant and e is the charge of an electron.
What is the major difference between the photoeffect and the Compton effect? All of the energy of the X-ray (or gamma) photon is used to ionize the atom and set the electron in motion in photoelectric effect. On the contrary, only part of the photon energy is used for these processes in Compton effect, and the photon having lower energy is scattered.
What is the minimal energy of a -photon needed for pair-production (not numerically)? The energy equivalent to the rest mass of an electron and a positron according to the Einstein mass-energy 2 equivalence equation: E=(me+mp)c , where me and m p are the rest masses of an electron and a positron, respectively, c is the speed of light in vacuum and E is the minimal energy of a -photon inducing pair production.
Define the term and unit of voltage! The voltage between points A and B is the difference between the electric potentials of points A and B. The unit of voltage is volt (V). If the voltage between points A and B is 1V (U B-U A=1V), the amount of work required to move a charge of 1 coulomb from point A to B is 1 joule.
Define electric current and derive its unit from other SI units! Electric current is the amount of charge transported across a boundary per unit time. Its unit is ampere (A). coulomb A second
Define resistance and give its unit! According to Ohm’s law resistance (R ) of a piece of conducting material is the ratio of the voltage applied across the piece of material (U ) and the current through the material (I ): U R I V ). The unit of resistance is ohm (
A Define what electric dipole is, and describe how to calculate its electric dipole moment! An electric dipole is a separated pair of -q -q positive charge (+q) and an equal amount of negative charge (-q). The electric dipole moment ( p) is defined by the following equation: p q r , where r is the separation distance between the
charges. Electric dipole moment is a vector quantity pointing from the negative charge towards the positive one.
2 Atomic physics, electromagnetic waves, X‐ray 20.
h f c h ,
What is annihilation? The process in which an electron and a positron (or in general a particle-antiparticle pair) collide with each other and the total mass-energy of this particle system is converted to the energy of two gamma photons, is called annihilation.
What is the difference between the orbital and spin angular momenta of an electron? - the orbital angular momentum originates from the orbital motion of an electron; its magnitude depends on the shape of the orbital and the interactions of the electron with the surrounding particles. - the spin angular momentum is an inherent property of the electron, its magnitude is independent of the surroundings. Align in ascending order the following components of the electromagnetic spectrum according to their energy: microwaves, gamma, ultraviolet, visible light, X-ray, infrared, radiowaves! radiowaves < microwaves < infrared < visible light < ultraviolet < X-ray, gamma
responsible for the absorption of and X-rays ! - photoelectric effect - Compton-effect - pair-production
where h and c are
Planck’s constant and the speed of light in vacuum, respectively, and is the wavelength of the photon. 21.
28. Why is a heavy nucleus necessary for pair- production? The presence of a heavy nucleus is required by the law of conservation of momentum.
Give the energy and momentum of a photon with frequency f. The energy of a photon with frequency f is hf , and its
What is the definition of visible light? The range of electromagnetic radiation observable by the human eye (approximately 400-750 nm).
Define interference! Interference is the superposition of waves that results in the generation of a new wave pattern.
What is constructive and destructive interference? Interference is constructive when the amplitude of the resultant wave is greater than the amplitudes of the individual waves, and it is destructive when the amplitude of the resultant wave is less than that of the individual waves.
What is the requirement for maximally constructive and maximally destructive interference if two propagating waves with identical wavelength interfere with each other? Maximally constructive interference takes place, if the path difference (s) between the waves is an integer multiple of the wavelength ( ): s l , where l=0,1,2,3…. This happens when the crest of one of the waves is superimposed on the crest of the other one.
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Maximally destructive interference is generated, if
1 s l , 2
c - concentration in mol/liter L - optical path length.
i.e. when the crest of one of the 44.
What does the molar extinction coefficient depend on? It depends on the type of the absorbing material, the wavelength of the light, temperature, the type of the solvent and the environment.
How many fold does the intensity of light decreases if the absorbance (optical density, extinction) of a solution is 1? It decreases 10-fold.
What is the definition of the molar extinction coefficient? It is the absorbance (optical density) of a solution with a concentration of 1M and an optical path length of 1 cm.
At what wavelength are the characteristic absorption maxima of proteins and nucleic acids? proteins 280 nm, nucleic acids 260 nm
What is monochromatic light? Light is monochromatic if its spectrum consists of a single wavelength only
Which amino absorption? Tyr, Trp, Phe
What kind of special characteristics does laser light have? - monochromatic - coherence in time and d istance - small divergence - high light density.
What is the definition of a singlet and a triplet state? In a singlet and a triplet state the number of unpaired electrons is zero and two, respectively. In a singlet and a triplet state, the value of the resultant spin multiplicity is 1 and 3, respectively.
What are the possible ways of relaxation of an excited electron in a molecule? (List at least 5 of them!) - vibrational relaxation - internal conversion - intersystem crossing - fluorescence - phosphorescence - delayed fluorescence - energy transfer to another molecule.
What is the definition of fluorescence lifetime? The time during which the number of excited molecules decreases to 1/e-times (37 %) of its initial value.
What is a., scintillation, b., chemiluminescence, c., photoluminescence? Processes where photon emission is elicited by a., ionizing radiation b., chemical reaction c., excitation by photons.
How can fluorescence quantum efficiency (yield) be defined? The fraction of excited molecules emitting a fluorescent photon, or the number of fluorescence photons divided by the number of absorbed photons, or the rate constant of fluorescence divided by the rate constants of all possible deexcitation processes.
Why is the fluorescence quantum yield always smaller than one? Because relaxation from the excited state can be accomplished not only by fluorescence emission.
What is the lifetime range of fluorescence? = 10-9 – 10-7s
What is the lifetime range of phosphorescence? = 10-6 – 10 s
waves is superimposed on the trough of the other one. 34.
Give the condition for constructive interference for an electromagnetic wave with wavelength diffracted on a crystal with a grating constant of c! o (angle of incidence is 90 ) c cos=l , where l=0,1,2,3,...n, =angle of diffraction How can the overdetermination of the Laue equations be resolved in the case of a three dimensional crystal? Either by rotating the crystal or making powder of it.
What is the definition of transverse and longitudinal waves? In a transverse wave the displacement of oscillating particles is perpendicular to the direction of propagation of the wave. In a longitudinal wave the displacement is parallel to the direction of propagation.
3 Absorption, luminescence, lasers 36.
List the types of interactions laser light can have with tissues! photothermal (laserthermy, coagulation, vaporization, carbonization) fluorescence, photochemical reactions photodissociation multiphoton ionization
When is electromagnetic radiation coherent? If it consists of photons capable of forming observable interference fringes.
What basic phenomena is the generation of laser emission based on? - population inversion is needed for light amplification to occur, and it is only possible in systems with 3 or more energy levels - stimulated emission is needed to give rise to coherent monochromatic light. What is the approximate coherence length of a laser and that of a classical light source? 10 10 cm and a couple of cm, respectively
42. Align in ascending order the following transitions according to their energy difference: vibrational, rotational and electronic! rotational < vibrational < electronic 43. Write the Lambert-Beer law and interpret the variables in the formula! J c L lg 0 cL A or J J 0 10 J J - intensity of light after passing through a material with thickness L J o- incident intensity of light when it enters the sample A – absorbance (optical density or extinction) - molar extinction coefficient
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57. Why is phosphorescence lifetime longer than fluorescence lifetime? Because phosphorescence is the result of spinforbidden transitions. 58.
What are the requirements of Förster-type resonance energy transfer? -the separation between the donor and the acceptor has to be in the range of 2-10 nm -there has to be an overlap between the emission spectrum of the donor and the excitation spectrum of the acceptor -the relative orientations of the donor and the acceptor have to be adequate.
What can Förster-type resonance energy transfer be used for in biology? For measuring inter- and intramolecular distances. What is photoselection? I t is the selection of an oriented subpopulation from a randomly oriented population of molecules by linearly polarized light.
What is linearly polarized light? Light in which the electric vectors of all photons point in the same direction.
List at least five parameters which can be determined using fluorescent measurements! - DNA, RNA, protein and lipid content of a cell, or the quantity of any kind of material that we tagged with a fluorescent label. - permeability of the cell membrane - intracellular enzyme activities - membrane potential - intracellular calcium level - intracellular pH - presence and density of cell surface antigens and receptors - mitochondrial potential and the number of mitochondria per cell.
Geometrical optics, microscopy, electron microscopy
Define the index of refraction! The index of refraction (n) gives the speed of light (c ) in a given material according to the following equation:
What is numerical aperture? It is the product of the index of refraction of the material between the object and the objective (n), and the sine of the half angle of the objective (sin): n sin.
Give the formula for the resolving power of a conventional light microscope! 1 2n sin f d
where: n = refractive index of the medium between the coverslip and the objective, = half angle of the objective, = wavelength of light, d = the minimum distance between two points at which they are resolvable. 70.
What is the function of the dichroic mirror in a fluorescence microscope? It reflects the excitation light, and is transparent for the emitted photons, therefore it separates the excitation and emission light paths.
What is the function of the excitation filter in a fluorescence microscope? It is transparent only in the wavelength range in which the fluorescent dye can be excited, therefore it allows only those photons to reach the sample which can excite the fluorescent molecule.
What is the function of the emission filter in a fluorescence microscope? It is transparent only in the wavelength range in which the fluorescent dye emits photons, therefore only the photons emitted by the fluorescent dye will reach the detector.
List the imaging aberrations in optical systems! -chromatic aberration -spherical aberration -astigmatism -coma -curvature of the field of the image -barrel-shaped and cushion-shaped distortion of the image
Give the equation for the relationship between the image distance (i), object distance (o) and the focal distance (f)!
, where c 0 is the speed of light in vacuum.
Write Snell’s law of refraction! A light beam is refracted when it travels from a material with a refractive index of n1 into a material with a refractive index of n2 (n2 n1). Refraction is described by the following equation:
, where and are the angles of
incidence and refraction, respectively, c 1 and c 2 are the speeds of light in the two materials. 66.
How can the resolving power of a microscope be increased? -by decreasing the wavelength of light -by increasing the index of refraction of the material between the objective and the object -by increasing the half angle of the objective
Why is Förster type resonance energy transfer a sensitive method for distance measurements? Because its probability is proportional to the inverse sixth power of the separation between the donor and the acceptor.
What is the shortest resolvable distance in a light microscope? approximately 200 nm
Give the definition and SI unit of diopter! D (diopter)=1/f, is the refractive power of the lens, where f is the focal length of a given lens. SI unit: 1/m.
76. What were those two discoveries that made construction of an electron microscope possible? -an electron can be regarded as a wave, and its wavelength is only a fraction of the wavelength of visible light -an electron beam can be focused with a magnetic field 77.
List at least three signals that can be detected during an electron microscopic measurement! -back-scattered electrons
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-secondary electrons -characteristic X-rays -Auger electrons -absorbed electrons -cathode luminescence -transmitted electrons 78.
What are the two types of electron microscopes? transmission electron microscope (TEM) scanning electron microscope (SEM)
What is the principle of transmission electron microscopy? A thin, typically 100 nm thick, sample is illuminated with an electron beam. The sample scatters a fraction of the electrons, i.e. the sample usually does not absorb the electrons. Using magnetic lenses an image is formed from the electrons going across the sample. The image is characteristic of the electron scattering properties of the sample.
What is the principle of scanning electron microscopy? The sample is scanned by a thin electron beam. Secondary electrons induced by the electron beam are detected on a pixel-by-pixel basis.
Nuclear physics, radioactivity
Give the definition of isotopes! Isotopes are the variants of a chemical element with a given atomic number whose mass numbers are different.
On what kind of energy level does a nucleon reside in a nucleus compared to the energy of a free particle? A bound nucleon has negative potential energy compared to a free particle.
List the types of radioactive radiation and characterize the particles constituting them! Alpha radiation consists of helium nuclei. Negative beta radiation ( ) is composed of electrons, whereas + positive beta radiation ( ) consists of positrons. Gamma radiation is an electromagnetic radiation consisting of high energy photons.
What is the direction of changes in the atomic number and the mass number of nuclei during alpha, both types of and gamma decay? change in mass change in atomic number number decay 4 2 + 1 (in decay and 0 electron capture), decay +1 (in decay) 0 0 decay
Why is the spectrum of beta decay continuous? Besides an electron (or a positron) an antineutrino (or a neutrino) is also emitted, and the energy released during the decay is shared randomly between the two particles.
What is electron capture and what does it produce? Some nuclei are capable of capturing an electron residing on the K shell decreasing their atomic number by one. The vacancy generated this way on the K shell is filled by an electron from a higher shell. This transition generates characteristic X-ray and/or an Auger electron.
List the isotopes of hydrogen with their mass number and the constituents of their nuclei!
Hydrogen Deuterium Tritium 83.
Mass number 1 2 3
Composition 1 proton 1 proton+1 neutron 1 proton+2 neutron
What is the mass defect of nuclei? The mass defect equals the difference between the mass of a nucleus and the total mass of its constituents (Z: the number of protons and A-Z: the number of neutrons, where Z and A are the atomic number and the mass number of the nucleus, respectively): m = (Z mproton + [A-Z] mneutron) - matom where m is the mass defect, mproton, m neutron and matom are the masses of a free, unbound proton, a free, unbound neutron and the given atomic nucleus, respectively. What is the relationship between the total binding energy ( E) and the mass defect ( m) of a given nucleus? E=mc2, according to Einstein's mass-energy equivalence principle (c is the speed of light in vacuum).
Describe how the binding energy per nucleon changes as a function of mass number. Binding energy per nucleon has a maximum at nuclei with mass numbers 55-60 (i.e. Fe).
What are the properties of nuclear force (their range, strength and direction)? Nuclear forces have limited range, their effect is negligible at a distance of more than a single nucleon and they are independent of charge. They are very powerful attractive forces whose magnitude exceeds that of electrostatic forces.
92. Give the equation describing the number of undecayed nuclei as a function of time (i.e. the law of radioactive decay) .
N 0 e t
N0: number of radioactive nuclei at t=0, N: number of undecayed radioactive nuclei at the time of investigation, : decay constant, t: time. 93.
What is the physical meaning of the radioactive decay constant? Radioactive decay constant is equal to the inverse first power of the mean lifetime of a radioactive nucleus.
What is the relationship between the radioactive decay constant ( ) and the half life (T)? ln 2 T ln 2: the natural logarithm of 2.
Define biological half life. Biological half life is the time period during which half of the initial quantity of the radioactive isotope leaves the living system undecayed due to metabolism, secretion or excretion.
Define effective half life. Effective half life gives the time during which the initial activity of a given type of radioactive nucleus decreases to half of its original value either by physical decay or metabolism. or alternatively
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Effective half life gives the time period during which the number of the udecayed nuclei decreases to half of the original value either by physical decay or biological processes. One of the definitions is enough to asnwer the question. 97.
Describe the relationship between the effective (T eff ), the physical (T phys ) and the biological (T biol ) half lives! 1 1 1
Describe the relationship between the physical ( phys ), the biological ( biol ) and the effective ( eff ) decay constants! eff = phys + biol
Interaction of radiation with material, detection of radiation Write the formula describing the attenuation of gamma or X-ray radiation in an absorbing material.
J 0 e x
where J 0 denotes the incident intensity and J is the transmitted intensity after passing through an absorber of thickness x . µ is the absorption/attenuation coefficient. 100. What is the definition of the attenuation coefficient of a material for gamma or X-ray and what is its SI unit? The attenuation coefficient is the reciprocal of the distance at which the intensity of the radiation decreases to 1/e-times (37%) of the initial value. [µ]=1/m. 101. How does the intensity of -radiation change as a function of the distance from the radiation source? It is constant in the beginning then suddenly decreases to zero. 102. What is responsible for the energy loss of an alpha particle along its path? Ionization. 103. What kind of radioactive radiations can be detected by a GM-counter? -, - and -particles can be detected. 104. What is the basic principle of operation of a photomultiplier tube? Electrons liberated from a light sensitive cathode by photons are accelerated in an electric field and collide into other electrodes (dynodes) whose potentials are increased in succession along the length of the tube. The energy of this collision is sufficient to free several secondary electrons. In this way the number of electrons increases at each dynode. 105. What is the basic operation principle of ionization detectors? Electrons and positive ions produced by the ionization process are separated by the electric field of the detector. The charged particles are attracted towards the appropriate electrodes and generate electric impulses. 106. What is the principle of detection of radioactive radiation by a scintillation detector?
In certain organic and inorganic substances the energy of radioactive particles is converted to luminous energy, i.e. they generate visible light flashes. 107. List the radioactive radiations in order of increasing penetrability!