Glossary of biophysics

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20. Give the energy and momentum of a photon with frequency f.
The energy of a photon with frequency f is hf, and its
momentum is hf ch, where h and c are
Planck’s constant and the speed of light in vacuum, respectively, and  is the wavelength of the photon.

21. 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
What is the definition of visible light?
The range of electromagnetic radiation observable by the human eye (approximately 400-750 nm).
What is the wavelength range of ultraviolet radiation?
10nm – 400nm
25. What is the wavelength range of infrared radiation?
750nm – 1mm
Define the limiting frequency (fmax) of braking radiation at an accelerating voltage of U.
f eU 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.
28. 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 equivalence equation: E=(me+mp)c2, where me and mp 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.
29. Why is a heavy nucleus necessary for pair- production?
The presence of a heavy nucleus is required by the law of conservation of momentum.
30. 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.
31. List the three most important mechanisms
responsible for the absorption of  and X-rays
- photoelectric effect
- Compton-effect
- pair-production

32. Define interference!
Interference is the superposition of waves that results in the generation of a new wave pattern.
33. 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.
34. 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 , wherel=0,1,2,3.... This happens when the crest of one of the waves is superimposed on the crest of the other one. Maximally destructive interference is generated, if
sl2, i.e. when the crest of one of the
waves is superimposed on the trough of the other one.

35. Give the condition for constructive interference for
an electromagnetic wave with wavelength  diffracted on a crystal with a grating constant of c! (angle of incidence is 90o)
c cos=l , where l=0,1,2,3,...n, =angle of diffraction
36. 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.
38. What is monochromatic light?
Light is monochromatic if its spectrum consists of a single wavelength only
39. What kind of special characteristics does laser light have?
- monochromatic
- coherence in time and distance - small divergence
- high light density.

40. List the types of interactions laser light can have with tissues!
- photothermal (laserthermy, coagulation, vaporization, carbonization)
- fluorescence, photochemical reactions
- photodissociation
- multiphoton ionization

41. When is electromagnetic radiation coherent?
If it consists of photons capable of forming observable interference fringes.
37. 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.
42. 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.
43. What is the approximate coherence length of a laser and that of a classical light source?
1010 cm and a couple of cm, respectively
44. Align in ascending order the following transitions according to their energy difference: vibrational, rotational and electronic!
rotational < vibrational < electronic
45. Write the Lambert-Beer law and interpret the variables in the formula!
log J/Jo = CEL = A or J =Jo x E mu~ -CEL

J- intersitive after passing by a material with thickness L
Jo- incident intensity of light when it enters the sample A – absorbance (optical density or extinction)
 - molar extinction coefficient
c - concentration in mol/liter
L - optical path length.

46. 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.
47. How many fold does the intensity of light decreases if the absorbance (optical density, extinction) of a solution is 1?
It decreases 10-fold.
48. 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.
49. At what wavelength are the characteristic absorption maxima of proteins and nucleic acids?
proteins 280 nm, nucleic acids 260 nm
50. Which amino acids have reasonably high absorption?
Tyr, Trp, Phe
51. 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.
52. 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.

53. 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.
54. 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.

55. 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.
56. Why is the fluorescence quantum yield always smaller than one?
Because relaxation from the excited state can be accomplished not only by fluorescence emission
57. What is the lifetime range of fluorescence?
58. What is the lifetime range of phosphorescence?
=10-6 –10s
59. Why is phosphorescence lifetime longer than fluorescence lifetime?
Because phosphorescence is the result of spin- forbidden transitions.
60. 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.

61. 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.
62. What can Förster-type resonance energy transfer be used for in biology?
For measuring inter- and intramolecular distances.
63. What is photoselection?
It is the selection of an oriented subpopulation from a randomly oriented population of molecules by linearly polarized light.
64. What is linearly polarized light?
Light in which the electric vectors of all photons point in the same direction.
65. 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
- mitochondrial potential and the number of
mitochondria per cell.

66. 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:
c  c0 , where c0 is the speed of light in vacuum.
67. 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:
sinc1 n2 , where  and  are the angles of sin c2 n1
incidence and refraction, respectively, c1 and c2 are the speeds of light in the two materials.

68. What is the shortest resolvable distance in a light microscope?
approximately 200 nm
69. 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

70. 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.
71. Give the formula for the resolving power of a conventional light microscope!
f  1  2nsin d
72. 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.
73. 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.
74. 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.
75. List the imaging aberrations in optical systems!
chromatic aberration -spherical aberration -astigmatism
-curvature of the field of the image
-barrel-shaped and cushion-shaped distortion of the image

76. Give the equation for the relationship between the image distance (i), object distance (o) and the focal distance (f)!
111 iof
77. 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.
78. 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
79. List at least three signals that can be detected during an electron microscopic measurement!
-back-scattered electrons
-secondary electrons
-characteristic X-rays -Auger electrons -absorbed electrons -cathode luminescence -transmitted electrons

80. What are the two types of electron microscopes?
transmission electron microscope (TEM) scanning electron microscope (SEM)
81. 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.
82. 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.
83. Give the definition of isotopes!
Isotopes are the variants of a chemical element with a given atomic number whose mass numbers are different.
84. List the isotopes of hydrogen with their mass number and the constituents of their nuclei!
Mass number
1 proton
1 proton+1 neutron
1 proton+2 neutron

85. 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, mneutron and matom are the masses of a free, unbound proton, a free, unbound neutron and the given atomic nucleus, respectively.

86. What is the relationship between the total binding energy (E) and the mass defect (m) of a given nucleus?
E=mc2, according to Einstein's mass-energy equivalence principle (c is the speed of light in vacuum).
87. 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).
88. 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.
89. 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.
90. 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.
91. 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 number

change in atomic number
 decay
 decay
1 (in + decay and electron capture), +1 (in - decay)
 decay

92. 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.
93. 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.
94. Give the equation describing the number of undecayed nuclei as a function of time (i.e. the law of radioactive decay) .
N  N0et
N0: number of radioactive nuclei at t=0,
N: number of undecayed radioactive nuclei at the time of investigation,
: decay constant,
t: time.

95. 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.
96. What is the relationship between the radioactive decay constant () and the half life (T)?
T  ln2 
ln 2: the natural logarithm of 2.
97. 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.
98. 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
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.

99. Describe the relationship between the effective (Teff), the physical (Tphys) and the biological (Tbiol) half lives!
Teff Tphys Tbiol
100. Describe the relationship between the physical
(phys), the biological (biol) and the effective (eff) decay constants!
eff = phys + biol
101. Write the formula describing the attenuation of gamma or X-ray radiation in an absorbing material.
J  J0ex
where J0 denotes the incident intensity and J is the transmitted intensity after passing through an absorber of thickness x. μ is the absorption/attenuation coefficient.
102. 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.
103. 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
104. What is responsible for the energy loss of an alpha particle along its path?
105. What kind of radioactive radiations can be detected by a GM-counter?
-, - and -particles can be detected.
106. 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.
107. 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.
108. 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
109. List the radioactive radiations in order of increasing penetrability!
110. What is the biological effect of radioactive radiation based on?
Excitation and ionization of atoms and/or molecules of living systems
111. What kind of particles are able to produce a biological effect in radiation biology?
Particles giving their energy partially or totally to the biological object are able to produce a biological effect.
112. What is a hit in radiation biology?
If one or more ionizations are produced in the radiosensitive volume of a biological object.
113. How can a dose-response curve be constructed?
The applied radiation dose is plotted on the horizontal axis and the ratio of the surviving organisms (N) and the total number of organisms before irradiation (N0) is plotted on the vertical axis.
114. What is the probability of generating exactly ‘n’ hits when applying a dose of D in volume V?
P n
VDn n!

115. How does the number of ionizations depend on the dose of the radiation?
The number of ionizations is linearly proportional to the dose.
116. Write the equation describing the dose-response curve when one hit is necessary for inactivation?
N eVD N0
117. What is D37?
D37 denotes the dose at which 37 % of the irradiated objects survive. If one ionization causes inactivation, D37 corresponds to one hit in a radiosensitive volume (VD=1, that is D=1/V).
118. What is the principle of the indirect action of radiation?
In aqueous solutions a particle of an ionizing radiation most probably causes ionization of the solvent (water) because water molecules outnumber solute molecules.Radicals generated by the above process are responsible for damaging solute molecules. This way the target “gets bigger”.

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