General Biophysics

    • “Every organism must interact with its environment in order to obtain energy, and in many cases it acts on itself, as humans do. No organism can survive if isolated from its environment.”
    • “Although every single creature is damned to give up in its personal battle against chaos, life itself continues.”
    • “Life involves a temporary decrease of entropy for which energy is spent.”
    • “Life is an irreversible process. An organism which obtains equilibrium with its environment is dead. (….) Universe is an isolated system. (….) In a certain sense we buy our lives through entropic death of universe.”

 

      from

Biochemistry

    , by C.K.Mathews and K.E.van Holde
    • Some definitions
      • vacuum : the unmaterial component in universe
      • matter : everything that occupies a space and has a mass in the universe
        • object : a part of matter
        • atomic theory : the theory that the molecules of a substance are made up of one or more atoms, each representing a definite amount of the element, which amount does not vary in the molecule, whatever combinations the molecule may enter.
        • electron theory : all bodies are complex structures composed of small particles called atoms together with still smaller particles called electrons.
        • particle : the minimum unit of matter that mantains the chemical properties of a chemical element (i.e. : the atom) or of a chemical compound (i.e.: the molecule). Molecules form when atoms team up, glued together by electrons that smear themselves into orbitals, which define the area where each electron is most likely to be found. When these molecules react, the electrons shift their allegiances between different atoms and change the shape of the molecular orbitals. An approximate take on quantum mechanics tells you that you can’t directly observe an orbital, yet we have. The imaging technique uses extremely short laser pulses to briefly ionize an electron away from a molecule of nitrogen, which is simply 2 nitrogen atoms stuck together (N2). As they spring back, the electrons emit light that can interfere with the laser pulse in different ways depending on the electron’s position and where the laser pulse hit the molecule. Measuring this interference for thousands of ionizations allowed the scientists to reconstruct the shape of the outermost electron orbital in nitrogen. It produces a blurred image, like a swarm of flies snapped in a long-exposure pictureref. The electron is pulled out of position by the laser pulse’s oscillating electric field. This field cycles from high to low and back again every 2 femtoseconds, which is fast enough to catch electrons moving around during chemical reactions as well. Although the scientists have only looked at a simple, linear nitrogen molecule so far, early results suggest that this will be possible with more complex molecules. The technique could eventually help chemists to improve existing chemical reactions, design new catalysts or even understand how biological processes work. Protein folding, for example, relies on subtle interactions between atoms and electrons that many scientists are now trying to simulate with computersref.
        • substance : a group of particles. If all particles are identical, it is a pure or simple substance, otherwise it is a complex substance
          • magnet : a lodestone; native iron oxide that attracts iron; also a bar of steel or iron that attracts iron and has magnetic polarity.
            • permanent magnet : one with permanent magnetic qualities
            • temporary magnet : a substance that possesses magnetic properties only during the passage of an electric current or when a permanent magnet is near it.
            • magnetization : the act or process of rendering an object or substance magnetic.
              • longitudinal magnetization : the component of a magnetization vector that is parallel to the direction of the magnetic field.
              • transverse magnetization :  the components of a magnetization vector that are in a plane perpendicular to the direction of the magnetic field
      • physics : the science that studies transformations in which no qualitative change in substances occurs
      • chemistry : the science that studies transformations in which qualitative changes in substances occur
      • system : a group of objects which can exchange with other systems …
        • … both mass and energy (open system) ;
        • … only energy (closed system) ;
        • … neither mass nor energy (isolated system).

Also, it may be …

        • … physically homogeneous …
          • … and chemically homogeneous : pure or simple substance
          • … and chemically heterogeneous : solution (solute + solvent)
        • … physically heterogeneous (i.e. : at least 2 phases are distinguishable) …
          • … and chemically homogeneous
          • … and chemically heterogeneous (mixtures)
            • if liquid + solid : suspension
            • if liquid + liquid : emulsion
            • if solid + solid : alloy
        • … physically semi-homogeneous and chemically semi-homogeneous (colloid or colloidal solution)
          • if liquid + thin solid : sol —–coagulation—–> liquid inside solid : gel
          • if gas + (aerosol or spray) …
            • … liquid : fog
            • … thin solid : smoke
            • together they create smog.
      • conversion : a shift from one form or state to another
        • gas liquefaction / condensation : the conversion of gas into a liquid form, brought about by cooling and compression, resulting in a decrease of the average kinetic energy of the molecules sufficiently to allow intermolecular forces of attraction to pull the molecules together
        • evaporation : conversion of a liquid or solid into vapor
      • Prefixes at Weizmann Institute

     

      • Fundamental (or universal) constants in physics
        • h (Planck’s constant) : 6,6260755 x 10-34 [J x s]
        • G0 (Cavendish’s constant) : 6,67259 x 10-11 [N x m2 / kg2]
        • c (light speed in vacuum) : 2,99792458 x 108 [m/s]
      • undulatory or wave theory : the theory that light, heat, and electricity are transmitted through space in the form of waves.
      • Planck’s quantum theory : the theory that the radiation and absorption of energy take place in definite quantities called quanta (E) which vary in size and are defined by the equation E = hn, in which h is Planck’s constant and n is the frequency of the radiation.

     

      • SI base units : any of the units of the Système International d’Unités, or International System of Units, adopted in 1960 at the Eleventh General Conference of Weights and Measures. SI units are based on the metric system and many are derived from natural constants. For units and for multiples and submultiples of these units formed by the use of prefixes
          • CGS unit : any unit in the centimeter-gram-second system.
        • mass units
          • mole (mol) is an amount of substance that contains as many objects (molecules, particles, ions, cells etc.) as the number of atoms in exactly 12 grams of 12C. This number can be determined experimentally to be 6.022 x 1023 (602,200,000,000,000,000,000,000), a number which is called Avogadro’s number. The mole is simply a convenient unit for dealing with large numbers just like it is easier to talk about the weight of a ship in tons rather than ounces.
          • atomic weight or mass unit (amu) (u) / dalton is defined by setting the mass of one 12C atom equal to 12 amu. We can determine the amu experimentally to be 1.657 x 10-24 (0.00000000000000000000000166) grams. Just as Avogadro’s number is very large, an amu is very small.
          • metric ton (t) : a metric ton is equal to 1,000,000 grams = 1,000 kilograms = 2,204 pounds = 1.102 U.S. short tons.
          • gram (g, gm) : a gram is 1/1000th of a kilogram. A gram is equal to the mass of water contained in a cube one cm on each side (one cubic centimeter = 1 cc = 1 cm3 of water weighs 1 gram). 1 kg = 2.205 pounds. A cube of water 10 cm on each side has a mass of 1 kg.
            • gamma : an obsolete equivalent for microgram (mg)
          • carat (c) : used primarily for gemstones, one carat = 0.2 gram = 0.00705 ounce. There are 5 carats in 1 gram.
          • ton (long ton) : in the U.S., a long ton = 1.12 short tons = 2,240 pounds = 1.016 metric tons.
          • ton (short ton) : in the U.S., a ton is 2,000 pounds = 907.18 kilograms = 0.907 metric tons. This is the “ton” that most Americans use.
          • pound (lb, lbs) : the English unit of mass (weight) of both the avoirdupois and the apothecaries’ system. The avoirdupois pound contains 16 ounces, or 7000 grains (a less common unit), and is the equivalent of 453.592 gm. The apothecaries’ pound contains 12 ounces, or 5760 grains, and is the equivalent of 373.242 gm
          • ounce (oz, oz avdp) : 1 ounce is equal to 437.5 grains, 1/16 of a pound, or 28.350 grams. The system of having 16 ounces in a pound is called the avoirdupois system. Note: an ounce is a unit of weight that is not equal to a fluid ounce which is a measure of volume. The troy or apothecary weight system has one ounce = 480 grains = 31.103 grams and 12 ounces = 1 pound! That means one avoirdupois ounce is equal to 0.910 troy ounce.
          • dram (dr, dr avdp) : fairly uncommon. There are 256 drams in a pound. 1 dram = 27.34 grains = 1/16 ounces. Caution: apothecary drams and fluid drams are different from the avoirdupois dram (see previous entry).
          • grain (lb, lbs) : fairly uncommon. There are 480 grains in a troy ounce and 7,000 grains in a pound. 1 grain = 64.799 mg = 0.324 carats.
          • cloves and tods were units used in weighing wool — thus a clove equals 7  pounds, a stone equals 14 pounds, a tod equals 2 stone, a wey equals 6 and a half tod, a pack equals 240 pounds, a sack equals 2 weys, and a last equals 12 sacks.
        • energy units
          • electron volt (eV) : the electron volt is the energy that we would give an electron if it were accelerated by a 1 volt potential difference. 1 eV = 1.602 x 10-19 J. This term is most often used by physicists and electrochemists.
          • kilojoules per mole (kJ/mol, kJ.mol-1) : a Joule, J, is the SI unit of energy and is defined as one kg.m2/s2. The prefix “kilo” means 1,000, so one kJ = 1,000 J. As the energies associated with a single molecule or atom are quite small, we often find it easier to discuss the energy found in one mole of the substance, hence “per mole”. To get the energy for one molecule, divide kJ/mol by Avogadro’s number, 6.022 x 1023.
          • kilocalories per mole (kcal/mol, kcal.mol-1) : a calorie was originally defined as the amount of energy required to raise the temperature of one gram of water by one degree Celsius. One calorie = 4.184 J. One kcal = 1,000 cal. When we count calories in our food, we are actually referring to kilocalories; e.g. 1 dietary Calorie = 1,000 cal = 1 kcal. See the note in the previous entry for information about the mole part of this unit.
          • British thermal unit (BTU) : the amount of heat necessary to raise the temperature of 1 pound of water 1°F, usually from 39°F to 40°F
        • temperature scale : a scale used for expressing the degree of heat, based on absolute zero as a reference point (absolute scale), or with a certain value arbitrarily assigned to such temperatures as the ice point and boiling point of water under certain stipulated conditions, the range between and beyond them being divided into a designated number of identical units.
          • absolute temperature scale : one with its zero at absolute zero (-273.15°C, -459.67°F).
          • Celsius scale : a temperature scale on which 0° is officially 273.15 kelvins and 100° is 373.15 kelvins; abbreviated C or Cel. Before 1948 (and still, unofficially) the degree Celsius (°C) was called the degree centigrade (symbol °C) with 0° at the freezing point of fresh water and 100° at the boiling point, at normal atmospheric pressure (760 mm Hg).
          • Fahrenheit scale : a temperature scale, obsolescent but still commonly, unofficially used in the United States, in which the interval between Fahrenheit’s 2 original fixed points, which are the lowest temperature attainable by a freezing mixture of ice and salt (0°) and the normal temperature of the human body (96° originally), is divided into 96 degrees (96 having 10 factors besides itself and 1); fresh water freezes at about 32° and boils at about 212° under average atmospheric pressure
          • homigrade scale : a temperature scale in which 0° represents the melting point of ice (0°C, 32°F), 100°, normal human temperature (37°C, 98.6°F), and 270° the boiling point of water.
          • Kelvin scale : an absolute temperature scale whose unit of measurement, the kelvin, is equivalent to the degree Celsius, the ice point therefore being at 273.15 kelvins.
          • Rankine scale : an absolute scale on which the unit of measurement corresponds with that of the Fahrenheit scale, so that the ice point is at 491.67 degrees Rankine (°R)
          • Réaumur scale : a temperature scale with the ice point at 0 degrees and the normal boiling point of water at 80° Rankine (°R)
        • On the atomic scale, temperature is also a description of the distribution of heat energy among the many billions of atoms and molecules that make up the world around us. Crucially, this is a statistical approach that assumes you are dealing with very large numbers of particles. For just one atom, such an approach is not meaningful, says Atkins. The statistics only start to make sense when considering dozens, or even hundreds of atoms : it may also fail to apply in rather larger entities, such as carbon nanotubes (10-

    m

          m cylinders that could be used to make miniature electronic devices, containing < 100,000 atoms). The blossoming field of nanotechnology relies on being able to manipulate materials that are made from just a few thousand atoms

    ref

          .

    Web resources

          :

        • distance units
          • inch (in, U.S.) : there are 12 inches in a foot and 36 inches in a yard. 1 inch = 2.54 centimeters.
          • foot (ft, U.S.) : there are 12 inches in a foot and 3 feet in a yard. 1 foot = 30.48 centimeters = 0.3048 meters.
          • yard (yd, U.S.) : there are 3 feet = 36 inches in a yard. 1 yard = 0.9144 meters.
          • rod (rd, U.S.) : generally obsolete. A unit of length equal to 16.5 feet.
          • furlong (fur., U.S.) : traditionally used only in horse racing. A unit of length equal to 660 feet = 201.168 meters. There are 8 furlongs in 1 mile.
          • statute, survey, international or land mile (mi, U.S.) : there are 5,280 feet in 1 mile. 1 mile = 1.609344 kilometers = 1,609.344 meters. Caution: The nautical mile is 1.151 statute miles = 1.852 kilometers.
          • international nautical mile (naut mi); do not confuse with international mile. There are 6,076.1155 feet in 1 nautical mile. 1 nautical mile = 1.15078 statute miles = 1.852 kilometers = 1,852 meters.
          • meter (m, metric) : currently defined as the length of 1,650,763.73 wavelengths of the orange-red radiation of 86Kr in a vacuum. 1 meter = 39.37 inches = 3.28 feet = 1.09 yards.
          • angstrom (A, metric) : 1 Angstrom = 1 x 10-10 meters. 1 Angstrom = 100 pm = 0.1 nm. The bond distances between atoms are generally in the range of 1 to 3 Angstroms.
          • astronomical unit (au) : an astronomical unit is defined as the mean distance between the Earth and the Sun. 1 au = 149,597,870 kilometers = approximately 92.5 million miles.
          • light year (ly) : a unit of distance that would be traversed in a period of one year by an object moving at the speed of light in a vacuum (300,000,000 meters per second). 1 light year = 63,239.7 astronomical units = 0.3066 parsecs = 5.88 x 1012 miles. The nearest star system, Alpha Centauri, is 4.3 light years from ours.
          • parsec (par) : a unit of distance equal to the distance from the sun to a point having a heliocentric (sun-centered) parallax of one second (second as an angle, not a time unit). 1 parsec = 3.26164 light years. If you find this term on an MSDS, you really aren’t from around here, are you?

    Web resources

        :

    SI base units

        at Weizmann Institute

      • SI derived units at Weizmann Institute
        • area units :
          • acre (acre) : the area of a square measuring approximately 209 feet on a side. 1 acre = 43,560 square feet = 4047 sq meters = 0.4047 hectares
          • are (a) : the area of a square measuring 10 meters on a side. 1 are = 1076 sq feet = 100 sq meters = 0.01 hectares = 0.0247105 acres.
          • hectare (ha) : the area of a square measuring 100 meters on a side. 1 hectare = 2.47 acres = 10,000 sq meters = 0.01 sq kilometers.
        • volume units :
          • ounce (oz, U.S.) : one fluid ounce = 1/8 of a half-pint = 1/16 of a pint = 1/32 of a quart = 1/128 of a gallon. One fluid ounce = 29.5735 mL.
          • pint (pt, U.S.) : there are 2 half-pints = 16 ounces in a pint. There are 2 pints in a quart and 8 pints in a gallon. One pint = 473.176 milliliters.
          • quart (qt, U.S.) : there are 4 half-pints = 2 pints = 32 ounces in a quart. There are 4 quarts in a gallon. 1 quart = 0.94635 liters = 946.35 milliliters.
          • gallon (gal, U.S.) : there are 128 ounces = 8 pints = 4 quarts in a gallon. 1 gallon = 3.785 liters.
          • cubic inches (in3, cub. in., U.S.) : this is the volume occupied by a cube one inch on a side. 1 cubic inch = 16.387 cubic centimeters (cc and mL), There are 1728 cubic inches in one cubic foot.
          • cubic feet (ft3, cub. ft., U.S.) : this is the volume occupied by a cube one foot on a side. 1 cubic foot = 1728 cubic inches = 28,316.8 cubic centimeters (cc, cm3, mL)
          • cubic yard (yd3, cub. yd., U.S.) This is the volume occupied by a cube one yard on a side. 1 cubic yard = 27 cubic feet = 0.7646 cubic meters.
          • milliliter (mL, cc, cm3, metric) The prefix “milli” means 1/1000, so 1 milliliter = 0.001 liters. Alternatively, there are 1000 milliliters in a liter. One milliliter = 0.0338 fluid ounces. Also known as a cubic centimeter (see distance units) because a cube 1 cm on each side has a volume of 1 ml. Because water has a density of 1.0, 1 ml of water weighs 1 gram.
          • deciliter (dl, metric) : the prefix “deci” means 1/10, so 1 deciliter = 0.10 liters. (Try not to confuse this with the decaliter which is equal to 10 liters). There are 10 deciliters in a liter.
          • liter (l, metric) 1 liter is the volume of a cube that is 10 cm (1 deciliter) on each side (see distance units). There are 10 deciliters = 1,000 milliliters = 1,000 cubic centimeters = 1.057 quarts = 33.814 ounces in a liter. Because water has a density of 1.0, one liter of water weighs 1,000 grams = 1 kilogram.
          • cubic meter (m3, metric) : tis is the volume of a cube 1 meter (see distance units) on each side. 1 cubic meter = 1000 liters. Because water has a density of 1.0, 1 cubic meter of water weighs 1 metric ton = 1,000 kilograms = 1,000,000 grams
        • pressure units
          • pounds per square inch (psi / PSI / lb/in2 / lb/sq in) : commonly used in the U.S., but not elsewhere. Normal atmospheric pressure is 14.7 psi, which means that a column of air 1 square inch in area rising from the Earth’s atmosphere to space weighs 14.7 pounds.
          • atmosphere (atm) : normal atmospheric pressure is defined as 1 atmosphere. 1 atm = 14.6956 psi = 760 torr.
          • torr (torr) / mmHg : based on the original Torricelli barometer design, one atmosphere of pressure will force the column of mercury (Hg) in a mercury barometer to a height of 760 millimeters. A pressure that causes the Hg column to rise 1 millimeter is called a torr (you may still see the term 1 mm Hg used; this has been replaced by the torr). 1 atm = 760 torr = 14.7 psi . 1 mmHg = 1.36 cmH2O = 0.133 kPa = 0.0193 psi
          • bar (bar) : the bar nearly identical to the atmosphere unit. 1 bar = 750.062 torr = 0.9869 atm = 100,000 Pa.
            • millibar (mb or mbar) : there are 1,000 millibar in 1 bar. This unit is used by meteorologists who find it easier to refer to atmospheric pressures without using decimals. One millibar = 0.001 bar = 0.750 torr = 100 Pa.
          • pascal (Pa) : 1 pascal = a force of 1 Newton per square meter (1 Newton = the force required to accelerate 1 kilogram 1 meter per second per second = 1 kg/(m.s2); this is actually quite logical for physicists and engineers, honest). 1 pascal = 10 dyne/cm2 = 0.01 mbar. 1 atm = 101,325 Pascals = 760 mm Hg = 760 torr = 14.7 psi.
      • Weights and measures at Weizmann Institute

     

     

     

      • Driving forces in biological systems
        • membrane ionic theory : the theory that the resting potential difference between the inside and outside of the cell is related to (1) the thin, electrically insulating membrane between the cytoplasm and the interstitial conducting medium, which is poorly and variably permeable to diverse ions; (2) the presence of a metabolic cellular pump that promotes the efflux of sodium ions from the cell interior to the outside against its electrochemical gradient and, coupled with this, the influx of potassium ions into the cell against its ionic concentration gradient.
        • polarization-membrane theory : the theory that living, resting cells are surrounded by a semipermeable membrane lined by a series of electrical doublets, or dipoles, with negative charges on the inner and positive charges on the outer surface. When the membrane is electrically intact, its entire surface is surrounded by doublets, and is said to be polarized.
      • ground state : the condition of lowest energy of a nucleus, atom, or molecule, as opposed to the excited state.
      • excitation => excited state : the condition of a nucleus, atom, or molecule produced by the addition of energy to the system as the result of absorption of photons or of inelastic collisions with other particles or systems
        • metastable state : an excited state with an unusually long lifetime, ranging from 10-6 second to several minutes. An intermediate state between the ground and excited states, requiring additional energy before decay to the ground state can occur.
      • singlet state : the excited state occurring when one electron of a pair is excited to a higher energy level without changing its spin; it is unstable and can decay to either a ground state or a triplet state.
      • triplet state : the excited state resulting when an electron is activated by absorbing a photon, moves to an outer orbital of higher energy, with the electron spin parallel to that of the other unpaired electron; it is a long-lived state that cannot decay to a ground state unless the spin changes again
      • ionization : any process by which a neutral atom or molecule gains or loses electrons, thus acquiring a net charge, as the dissociation of a substance in solution into ions or ion production by the passage of radioactive particles
        • Townsend avalanche ionization : the multiplicative process in which a single charged particle, accelerated by a strong electric field, produces additional charged particles through collision with neutral gas molecules
      • ion : an atom or radical having a charge of positive (cation) or negative (anion) electricity owing to the loss or gain of one or more electrons. Substances that form ions are called electrolytes
        • dipolar ion / zwitterion : a dipolar ion, i.e., an ion that has both positive and negative regions of charge; amino acids, for example, occur as zwitterions in neutral solution, and the pH value at which the zwitterion state is at a maximum is the isoelectric point.
        • hydrogen ion : the nucleus of the hydrogen atom or a hydrogen atom that has lost its electron, H+; it bears a positive charge equivalent to the negative charge of the electron and is called a proton.
        • hydronium ion : the hydrated form, H3O+, in which the proton (hydrogen ion, H+) exists in aqueous solution; a combination of H+ and H2O.
      • ionic theory : a theory that, on going into solution, the molecules of an electrolyte either completely or partially break up or dissociate into two or more portions, these portions being positively and negatively charged electrically, the positively charged portions being different chemically from those negatively charged. When an electric current is passed through the solution of an electrolyte, the positively charged portions are attracted by the negative pole or electrode, and move toward it; the negatively charged portions are attracted by and migrate toward the positive electrode. From this property of moving toward one of the electrodes, these charged molecular fractions of electrolytes are called ions, from the Greek verb meaning “to move.”
      • cathode-ray tube : a vacuum tube in which the cathode rays are accelerated as a beam to form luminous spots on a fluorescent screen
      • hot-cathode tube : a vacuum tube in which the cathode is electrically heated to incandescence and in which the stream of electrons depends on the temperature of the cathode.
      • valve tube : a vacuum tube used to rectify an alternating current
      • photon : a quantum of electromagnetic radiation. It has no charge and zero rest mass.
      • photomultiplier tube (PMT) : a vacuum tube that converts electromagnetic radiation signals into electrical pulses, consisting of a light-sensitive surface that emits electrons when light is incident on it, the electrons then passing through successive stages with electron multiplication at each stage.
      • electromagnetic units : that system of units based on the fundamental definition of a unit magnetic pole as one which will repel an exactly similar pole with a force of one dyne when the poles are 1 cm apart.
      • electrostatic units (esu) / elektrostatische Einheit (ESE) (Ger) : that system of units based on the fundamental definition of a unit charge as one which will repel an equal and like charge with a force of one dyne when the 2 charges are 1 cm apart in a vacuum
      • fusion commonly occurs in stars like the Sun, where hydrogen atoms meld together to form helium and release huge amounts of energy in the process. Scientists have long believed that fusion has the potential to be an enormous source of power here on Earth. However, no one has yet been able to control fusion reactions because they only occur at temperatures and pressures similar to those found in stars. Or so scientists thought until 1989, when Stanley Pons and Martin Fleischmann of the University of Utah claimed to have created a new kind of fusion inside a small canister of water. Pons and Fleischmann claimed that when they ran an electrical current between 2 palladium plates separated by water containing deuterium, it created a small but measurable cold fusion reaction. In a highly publicized press conference in Utah, the scientists claimed that this ‘cold fusion’ had the potential to revolutionize the world’s energy production. Pons and Fleischmann’s claims were quickly debunked by other scientists, who pointed out numerous experimental errors in the measurements. But the idea of cold fusion lives on in movies and science fiction, and among a small cadre of researchers. Those researchers finally caught the ear of the US energy secretary, Spencer Abraham, who commissioned the review in August 2003 from the department’s science directorate. Although the reviewers remained sceptical, they were nearly unanimous in their opinion that the energy department should fund well-thought-out proposals for cold fusionref
      • radioisotopes : a particular radionuclide is specified by
        • atomic number [number of protons in nucleus]
        • atomic weight [total number of protons + neutrons in nucleus]
        • nuclear energy state [e.g., a lower-case m after the atomic weight to denote metastable states]
        • low-energy electrons (LEEs) :
          • conversion electrons of < 50 keV
          • Auger electrons are electrons ejected by radiationless excitation of a target atom by the incident electron beam. When an electron from the L shell drops to fill a vacancy formed by K-shell ionization, the resulting X-ray photon with energy EK – EL may not be emitted from the atom. If this photon strikes a lower energy electron (e.g., an M-shell electron), this outer electron may be ejected as a low-energy Auger electron. Auger electrons are characteristic of the fine structure of the atom and have energies between 280 eV (carbon) and 2.1 keV (sulfur). By discriminating between Auger electrons of various energies, a chemical analysis of the specimen surface can be made. Auger electron energies are closely related to the corresponding X-ray energy, and most usually are described in X-ray notation. For example, the Si KL1L2,3 transition, experimentally observed at 1620 eV, involves removal of an electron in the K shell allowing an electron from the L1 shell to descend with the emission of energy of 1690 eV. This energy can either be emitted as a Si-Ka X-ray, or it can by transferred to a third electron, in this case in the L2,3 shell, which has a binding energy of about 90 eV, ejecting it from the atom with an energy of around 1600 eV. The probability of Auger electron production increases as the difference between the energy states of the shells decreases. Light elements are more susceptible to the formation of Auger electrons by multiple ionizations. Thus the proportion of radiation emitted at characteristic wavelengths is lower than for heavier elements. The proportion of Auger emission is greater than 0.5 up to about Z = 30 (zinc). So, typically, one switches which transition is used as we move up the periodic table: KLL transitions for light elements, LMM after that, and then MNN. The Auger phenomenon is described by the fluorescent yield, w, which for K-radiation is defined as wk = nk / Nk, where wk = fluorescent yield, nk = number of X-ray photons emitted from the sample, and Nk = number of ionizations. Fluorescent yields for the light elements are generally less than 0.2 for the K-lines. The X-ray yield increases sharply with increasing Z and Auger electron yield decreases. Thus Auger electrons provide a good basis for analysis of light atoms. One might expect that X-ray intensities would be lower at low Z because of increased Auger electron production, but lower fluorescent yield compensates for easier ionization. Auger electrons are produced from depths of about a wavelength into the sample because their low energies make them easily reabsorbed. This makes Auger electrons particularly good for analysis of surface composition, but such analysis requires ultra-high vacuum to avoid absorptive losses. When SE and Auger yield is plotted as a function of energy; the Auger electrons appear as a slight dimple which is often enhanced for detection by taking the derivative of the curve (dN(E)/dE).

    Decays

        :

        • a-decay only
          • 210Po (t1/2 = 138.4 days)
          • 83212Bi (t1/2 = 1.0 hour; Emax = 6.09 MeV; mean penetration range = 0.04-0.1 mm; imageable)
          • 83213Bi (t1/2 = 45.7′; Emax = 5.87 MeV; mean penetration range = 0.04-0.1 mm; imageable)
          • 85211At (t1/2 = 7.2 hours; Emax = 5.87 MeV; mean penetration range = 0.04-0.1 mm; imageable)
          • 227Th(t1/2 = 18.6 days)
          • 232Th(t1/2 = 1.41 x 1010 years)
          • 235U (t1/2 = 7.1 x 108 years)
          • 93237Np

          • 92238U (>90% of all naturally occurring uranium)

          • 91241Am(t1/2 = 432.7 years; emits an a particle with energy of 5.49 MeV; also emits gamma and x-rays. Most intense gamma ray energy is 0.060 MeV)

          • 96242Cm (t1/2 = 163 days to 238Pu; 2 high-energy a particles : 6.07 and 6.11 MeV)

        • a and b-decays
          • 225Ac (t1/2 = 10 days; Emax = 5.83 MeV; mean penetration range = 0.04-0.1 mm; imageable)
        • b+ (positron)-decay only
          • 611C
          • 713N
          • 815O
          • 918F (t1/2 = 112′)
          • 2964Cu (t1/2 = 12.8 hours; b-decay => Emax = 0.657-0.571 MeV ; g-decay => Emax = 1.35 MeV)
          • 3576Br
          • 3577Br
          • 53124I
        • b- (negatron / electron)-decay only [Gr. [emacr]lektron amber, because an electric charge can be produced in amber by rubbing] : an elementary particle possessing the unit quantum of (negative) electric charge, 1.6 x 10-19 coulomb, with mass 1/1836 that of a proton, or 9.11 x 10-31 kilogram. Electrons can exist as atomic constituents or in the free state; flowing in a conductor they constitute an electric current; when ejected from a radioactive substance, they constitute beta rays; and when revolving about the nucleus of an atom they determine all of its physical and chemical properties except mass and radioactivity. Symbol e or e-.
          • emission electron : one of the electrons released from the atom during radioactive decay.
          • free electron : an electron which is not bound to the nucleus of an atom but may move from one atom nucleus to another.
          • valence electron : one of the electrons in the outermost shell of an atom and thus able to participate in chemical reactions and the formation of chemical bonds.
          • 13H (b-decay to 23He ; t1/2 = 12.35 years; Emax = 0.018 MeV)

          • 611C (t1/2 = 20′; Emax = 0.981 MeV)
          • 614C (t1/2 = 5568 years; Emax = 0.155 MeV)

          • 1532P ( t1/2 = 14.3 days; Emax = 1.71 MeV)
          • 1635S (t1/2 = 87.1 days; Emax = 0.167 MeV)
          • 2045Ca (t1/2 = 152-164 days; Emax = 0.260 MeV)
          • 3889Sr (t1/2 = 50.5 days; Emax = 1.46 MeV; half-value layer = 1 mm Pb)
          • 3890Sr (t1/2 = 29.1 years; Emax = 0.546 MeV)
          • 3990Y (t1/2 = 64 hours = 2.7 days; Emax = 2.28 MeV; mean range = 2.76 mm; not imageable)

          • 44106Ru (106Ru/106Rh is an example of secular equilibrium. The 106Ru parent (halflife 368 days) disintegrates via b- decay with a peak b particle energy of 39 KeV to radioactive daughter 106Rh. The 90-percentile distance (the distance from a source within which 90% of the energy is absorbed) in water for 106Ru is less than 0.008 mm, so these particles may be considered to be entirely absorbed in the 0.1 mm silver window. The primary contributor to therapeutic dose is the continuous spectrum of beta particles emitted in the decay of 106Rh (halflife 30 s). 106Rh disintegrates by b- decay with a mean beta energy of about 1.4 MeV and a maximum of 3.54 MeV to the stable element 106Pd. The 90-percentile distance for 106Rh b particles in water is 7.92 mm. Backscatter from the 0.7 mm thick silver backing of the applicator tends to soften the spectrum, while attenuation in the 0.1 mm silver window tends to harden the spectrum of b particles which are emitted from the concave surface to the applicator)
          • 53129I (t1/2 = 16,000,000 years; Emax = 0.150 MeV)

          • 212Pb (t1/2 = 10.6 hours; Emax = 0.57 MeV; mean penetration range in biological tissues : 0.6 mm; imageable)
          • 94238Pu (t1/2 = 86 years : medical and industrial uses for cardiac pacemakers and radioisotopic thermoelectric generators
          • 94239Pu (t1/2 = 14.4 years; Emax = 0.021 MeV; high-energy a particles emitted by its decay)
          • 94241Pu (t1/2 = 14.4 years; Emax = 0.021 MeV; decays primarily by beta particle emission to 241Am (a high-energy a particle emitter). However, a very small fraction decays to 237U
        • b- (negatron)- and g-decays
          • 1122NaCl (t1/2 = 2.6 years)
          • 1124Na (t1/2 = 15.1 hours; b-decay => Emax = 1.39 MeV; g-decay => E = 2.75-1.37 MeV)
          • 1942K (t1/2 = 12.4 hours; b-decay => Emax = 3.58-2.04 MeV; g-decay => E = 1.395 MeV)
          • 2047Ca (t1/2 = 4.7 days)
          • 56Mn (t1/2 = 2.6 hours)
          • 2659Fe-citrate (t1/2 = 44.6 days; b-decay => Emax = 0.460-0.26 MeV ; g-decay => Emax = 1.30-1.10 MeV)
          • 2757Co (t1/2 = 271.4 days)
          • 2758Co
          • 2760Co (t1/2 = 5.272 years; b-decay => Emax = 0.308 MeV ; 2 g-decay => max E = 1.33 and 1.17 MeV; half-value layer = 1.2 cm)

          • 2964Cu (t1/2 = 12.8 hours; b-decay => Emax = 0.657-0.571 MeV ; g-decay => Emax = 1.35 MeV)
          • 2967Cu (t1/2 = 2.6 days; Emax = 0.57 MeV; mean penetration range in biological tissues : 0.6 mm; imageable)
          • 3065Zn (t1/2 = 250 days; b-decay => Emax = 0.32 MeV ; g-decay => Emax = 1.11 MeV)
          • 3786Rb (t1/2 = 18.7 days)
          • 4194Nb (t1/2 = 20,000 years; b-decay => Emax = 0.470 MeV) ; g-decay => Emax = 0.703 and 0.871 MeV).
          • 99Mo (t1/2 = 66.7 hours)
          • 53131I (t1/2 = 8.05 days; b-decay => Emax = 0.81 MeV ; g-decay => Emax = 0.164 MeV; half-value layer = 0.3 cm; mean penetration range in biological tissues : 0.4 mm (up to 1-2 mm); imageable)
          • 54133Xe (t1/2 = 5.25 days)
          • 153Gd (t1/2 = 242 days)
          • 62153Sm (t1/2 = 47 hours = 2 days ; Emax = 1.3 . 10-13 J = 0.80 MeV; mean penetration range in biological tissues = 0.53 mm; imageable)
          • 71177Lu (t1/2 = 6.646 days; b-decay => Emax = 0.50 MeV; g-decay => Emax = 0.149 MeV; mean penetration range in biological tissues = 0.28 mm; imageable)
          • 75186Re (t1/2 = 89.25 hr = 3.8 days; b-/EC,1.069 MeV; mean penetration range in biological tissues = 0.92 mm; imageable)
          • 75188Re (t1/2 = 17.021 hr; b-,2.120 MeV; mean penetration range in biological tissues = 2.43 mm; imageable)
          • 192Ir (t1/2 = 74 days)
          • 79198Au (b-decay => Emax = ? ; g-decay => Emax = 0.41 MeV; t1/2 = 2.7 days; half-value layer = 0.33 cm Pb)
          • 80203Hg (t1/2 = 46.8 days)
        • Auger electrons : a low-energy electron emitted when an inner electron shell vacancy is created, such as by electron capture or internal conversion.
          • 53123I (t1/2 = 13 hours ; Emax = 0.159 MeV; mean range = 0.001-0.02 mm; not imageable)
          • 53125I (t1/2 = 59.9 days; Emax = 0.171 and 0.245 MeV ; half-value layer = 0.02 cm Pb; mean range = 0.001-0.02 mm; imageable)
          • 195mPt (t1/2 = 4.0 days; Emax = 0.13 MeV; mean range = 0.001-0.02 mm; not imageable)
        • Auger, b and g decays
          • 3167Ga (t1/2 = 78 hours = 3.3. days; Emax = 0.18 MeV; mean range = 0.001-0.02 mm; imageable)
        • g-decay only
          • 2451Cr (t1/2 = 27.7 days)
          • 3475Se ( t1/2 = 118.5 days)
          • 3885Sr (t1/2 = 65.0 days; Emax = 360 and 880 keV)
          • 4399mTc (g-decay to the ground state 99Tc (Emax = 0.293 MeV); Emax = 0.140 MeV = 2.3 . 10-14 J ; t1/2 = 6 hours)

          • 46103Pd (t1/2 = 17 days; Emax = )
          • 49111In (t1/2 = 67.2 hours)
          • 50117mSn (t1/2 = 13.6 days; Emax = 0.15856 MeV)
          • 55137Cs (t1/2 = 30.17 years; Emax = 0.137 to 0.651 MeV; 85% of all Cs-137 decays emit a 0.662 MeV g ray; half-value layer = 0.65 cm Pb)

          • 77192Ir (t1/2 = 64.2 days; Emax = 0.13-1.06 MeV; half-value layer = 0.6 cm Pb)
          • 80197Hg (t1/2 = 64.1 hours)
          • 81201Tl (t1/2 = 73.1 hours) => 201Hg
          • 88226Ra (t1/2 = 1620 years; Emax = 1.0 MeV; half-value layer = 1.66 cm Pb)
        • 3685Kr
        • 49113mIn
        • 55131Cs
        • 53132I (t1/2 = 70 days; Emax = 0.137 to 0.651 MeV)

    Radioisotopes decay

        : N

    t

        = N

    0.

        e

    -lt

        • half life (t1/2) = ln(0.5)/l
        • average life = 1/l

        => half-life = ln(0.5) x average life

    Elements that are of interest for nuclear medicine and radiation oncology applications

        :

      • Some quantities and equations that link them, including derived constants    [units of measure]
        • International Standard (SI) units are now defined in terms of absolute atomic quantities. Examples include the second, which is measured by cycles of radiation emitted by a caesium atom, and the metre, defined as the distance travelled by light in a certain fraction of a second. Kg, the standard unit of mass, remains the only basic measuring unit still defined by a unique artefact – a cylinder of platinum and iridium kept at the International Bureau of Weights and Measures (BIPM) near Paris. Nearly 100 copies are stored worldwide, and must be sent to Paris every few years for verification. If Avogadro’s number could be defined with an accuracy of 1 part in 100 million, then a kilogram could be defined in terms of atoms
        • t (time)    [s]
        • l (lenght)     [m]
        • r (radius)      [m]
        • S (section surface)      [m2]
        • V (volume)       [m3 = 103 L]
        • F (force)      [N]
        • F (Faraday constant) = NA x e = 96500     [C/mol]
        • f1->2 (molar unidirectional flow)     [mol/s]
        • F (overwhelming molar flow) = int(J x dS)     [mol/s]
        • NA (Avogadro’s number) = 6,023 x 1023   [mol-1] = the number of atoms in 12 g of 12C, the most common form of carbon
        • v (velocity of a chemical reaction)       [depending on the order of the reaction]
        • Q10 (thermic coefficient) = vT=x+10 / vT=x     [adimensional]
        • P (pressure) = F / S      [N/m2 = Pa]
        • Mi (molar concentration of an i ion) = mol/V [mol/L] (Mi< and Mi> indicate the M of the compartments in which Mi is minor and major, respectively)
        • e (electron charge) = 1,9 x 10-19      [C]
        • Q (capacity) = V/t = v x S      [(mol x m2)/s]
        • T (absolute temperature)      [°K]
        • calorie : any of several units of heat defined as the amount of heat required to raise the temperature of 1 kg of water 1°C at a specified temperature. The calorie used in chemistry and biochemistry is equal to exactly 4.184 J. Symbol cal. NOTE: There was formerly a distinction made between the “small calorie,” defined above, and the “large calorie,” written Calorie with a capital “C” and abbreviated Cal, which was equal to 1000 small calories or one kilocalorie. The use of the large calorie survives only in nutrition, where calorie, now usually written with a small “c,” means kilocalorie when specifying the energy content of foods.
          • large calorie / kilocalorie (kg-cal) : the calorie used in metabolic studies, being the amount of heat required to raise the temperature of 1 kg of water 1°C, specifically from 14.5° to 15.5°C at a pressure of 1 atm. Also used to express the fuel or energy value of food.
          • gram, small or standard calorie (g-cal) : the amount of heat required to raise the temperature of 1 gram of water 1°C, specifically from 14.5° to 15.5°C at a pressure of 1 atm
          • mean calorie : one one-hundredth of the amount of heat required to raise the temperature of 1 gram of water from 0° to 100°C.
          • International Table (IT) calorie : a unit of heat, equivalent to 4.1868 J.
          • thermochemical calorie : a unit of heat, equivalent to 4.184 joules
        • hT (viscosity at absolute temperature = T) = (F x dx) / (S x dv)     [kg/(m x s)]
        • km (Hagen-Poiseuille’s law constant) = (p x r4) / (8hT x l)      [(m4 x s)/kg]
        • b (oil-water distribution coefficient)       [adimensional]
        • Fm (massive flow) = Km x DP      [mol/s]
        • R (perfect gas constant) = 8,31        [J/(°K x mol)]
        • kB (Boltzmann constant) = R / NA = 1,37 x 10-23       [J/°K]
        • K (kinetic energy) = 1/2 m v2 =  kB x T x a/2     [J]
        • f (friction coefficient)     [s/(N x m3)]
        • Di (diffusion coefficient of an i ion) = (RT) / (NA x f) = (kB x T) / f       [m2/s]
        • Dmi (membrane diffusion coefficient of an i ion)      [m2/s]
        • kd (free diffusion coefficient) = – Di/dx       [m/s]
        • kdm (membrane diffusion coefficient) = Dmi x b     [m2/s]
        • Pi or kP (membrane permeability coefficient) = kdm / Dx = (Dmi x b) / Dx = -J/DM    [m/s]
        • J (flow velocity) = F/S = -Pi x DMi = – (b x Dmi x DMi) / Dx      [mol/(m2 x s )]
        • ke = – (F x Mi x Di) / (R x T x dx)        [(mol x C) / (m2 x s x J)]
        • z (ion valence)     [adimensional]
        • conductivity = z x ke       [(mol x C) / (m2 x s x J)]
        • s (membrane reflection coefficient) = (H2O moles passed – solute moles passed) / (moles of H2O passed)    [adimensional]
        • Dpc (cellular osmotic pressure) = Dp x s = MRTs        [kg/(m x s2)]
        • DVm (membrane voltage difference)      [V]
        • Ei (equilibrium potential for an i diffusable ion)     [V]
        • Wc (chemical work)      [J]
        • We (electrical work)      [J]
        • Ni (total number of membran channels for the i ion)
        • gi (open channel conductance)       [S]
        • P* (open channel likelihood) = (P* all activaction gate(s) are open) x (P* all inactivation gate(s) are closed)  [adimensional]
        • Gi (maximal membrane conductance for an i ion) = gi x N     [S]
        • gi (i ion membrane conductance) = Pi x F3 x Mi< x DVm) / (R2T2 x e -[zFDVm/(RT)]) = Gi x P* = gi x Ni x P*        [S]
        • C (electrical capacity) = Q / DV    [F]
        • Rsm (axolemm specific resistance)        [W x m2]
        • Rsi (axoplasm specific resistance)        [W x m]
        • rm (axolemm resistance) = Rsm / (2pr)      [W/m]
        • ri (axoplasm resistance) = Rsi / (pr2)    [W/m]
        • re (ECM resistance)       [W/m]
        • l (electrotonic decline space constant) = [rm / (ri + re)]1/2 = (rm/ri)1/2 = [r x (Rsm/2Rsi)]1/2        [m]
        • t or t1/2 (half-life)      [s]
        • tribology is the study of adhesion, friction, lubrication and wear of surfaces in relative motion
        • light sources :
          • primary light sources emitt propert light
            • incandescent : color depends on temperature (e.g. Sun, voltaic arch)
            • luminescent : low temperature (e.g. firefly)
              • fluorescence (t < 10-8 s)
              • phosphorescence (t > 10-8 s)
          • secondary light sources reflect light from primary light sources (e.g. Moon)
        • transparent bodies : according to transparency of forms on the opposite sides …
          • diafanous (e.g. glass)
          • translucid (e.g. polished glass)
        • photometry
          • Bunsen photometer : when (intensity . distance2) are identical, the oil spot on the paper is no longer viewed (subjective evaluation)
        • light flow (f) = (energy flux . relative visibility coefficient)  [cd . sr = lumen (lm)]
        • light intensity (I) = f / 4p [candle (cd)]. 1 cd = light intensity of a black body at P = Patm and T = Tfusion Pt over a surface = 6 . 10-5 m2
        • enlightnment intensity (E) over a spherical segmental surface = f / 4pr2 = I / r2 (Lambert’s law) = I0cosa / r2
        • luminance (L) over a flat surface = I / S [cd/m2 or nit]
        • absorption (I) = I0 . e -ax, where a = absorption coefficient, depending on l and rmedium
        • luminosity = Estrumental vision / Enaked eye vision
        • Raman effect : when a substance is irradiated with monochromatic light, the spectrum which the substance scatters contains, in addition to a line of the same wavelength as the incident radiation, lines which are satellites of the primary line moving with it when the wavelength of the primary radiation is altered.
        • geometric optics (when distances are >> l)

    Principles

          :

          • straight propagation of light and reciprocity of light ways
          • independence of light rays (perpendicular to wavefronts)
          • incident ray, reflexed ray, refracted ray and the line perpendicular to incidence point lies on the same plane
          • incident angle (î) = reflexion angle (ê)
          • when incident rays passes from a medium with lower refractive index to a medium with higher refractive index the refracted ray comes nearer to the line perpendicular to the incidence point, and viceversa
          • Fermat principle : the route followed by light ray joining point A to point B passing by dioptric media (eventually different) is that for which the optic way (ie the sum of the products of tracts and refractive indexes) is minimal, maximal or stationary
        • refractive index (n / nD) : the refractive power of a medium compared with that of air, which is assumed to be 1
          • absolute refractive index (n) = vvacuum / vmedium = c / vmedium. In solid and liquid media, n ~ 1/l. It is a measure of a clear substance’s ability to slow photons, and thereby bend the direction of travel of off-axis rays of light. The denser the material, the more it will slow photons, and therefore bend the direction of travel.
            • vacuum of space : 1.00000
            • air : 1.00029
            • distilled water : 1.33
            • tears : 1.3369
            • seawater (average) : 1.341
            • acrylic resins (plastic lenses) : 1.49
            • crown glass : 1.52
            • polycarbonate : 1.586
            • flint glass : 1.68
            • rare metals (Ln, Ni, Ta) : 1.88
            • diamond : 2.417
          • relative refractive index (n1,2) = n1/n2

    Refraction

          : n

    1,2

          = n

    1

          /n

    2

          = sen î / sen ê = v

    1

          /v

    2

          (

    Descartes’ or Snell’s law / law of sines

          )

          • reflexion : if v1 = v2 => sen î = sen ê

          At the separating surface between 2 different media, part of the light is reflexed, part is refracted, and part is absorbed. If the surface is irregular, diffusion occurs.

    Optic dispersion prism

          :

     

          AED triangle is similar to FOD triangle => EAF angle =

    a

          = FOD angle. For the external angle theorema

    d

          = GEF angle + GFE angle = (ê – FEO angle) + (î – EFO angle). As FEO angle + EFO angle = FOD angle =>

    d

          = ê – î -

    a

          . If

    a

          and î are small =>

    d

          = (n-1)

    .a

          . For a given opening angle

    a, d

          is minimal when î = ê.

     

          n

    1,2

          = sen î / sen ê = sen (

    dmin

          +

    a

          ) / 2] / sen(

    a

          /2) = 1 / n

    2,1

          . In this condition

    dmin

          = 2î -

    a

          => î = (

    dmin

          +

    a

          ) / 2. Furthermore FEO angle = EFO angle = ê => ê =

    a

          /2.

     

          deviation ~

    lmonochromatic radiation used
    Limit angle

    lim

          ) = arcsen(n

    1,2

          ) = that value of î for which ê = 90°, behind that

    total reflexion

          occurs

    Mirrors

          :

          • flat mirrors : reflected images have identical size, are right and virtual (q = -p). If 2 flat mirrors are neared with an angle = a, the total number of reflexed images = (360°/a) -1
          • curved mirrors
            • spheric mirrors
              • concave flat mirrors : according to bisectant theorema, IP : qI = rP : qr. As in Gauss conditions the opening angle is small, PI  ~ p and qI  ~ q => p:q = (p-r) : (r-q). As f = r/(2, by dividing both members of the equation for (p.q.r) => 1/p + 1/q = 1/f (conjugate point formula). The transverse enlargement (G) = | f | / ( | p – f |) = | q | / | p |
                • if p > r => reflected images are reduced, real, and viceversed, f < q < r (limit case : if p = r => q = r)
                • if f < p < r => reflected images are enlarged, real, and viceversed, q > r (limit case : if p = f => q = infinite)
                • if 0 < p < f => reflected images are enlarged, virtual, and right, on the same side of the object
              • convex flat mirrors (directed to side opposide to the center of the calotte. Rays are always divergent and reflected images are always right, reduced, and virtual.
            • cylindric mirrors modify images in all directions except that parallel to the axis
            • parabolic mirros reflect all rays coming from a source placed in the focus parallel to the axis, and viceversa

          Electric field vectors of light can be decomposed into components perpendicular and parallel to the inciding plane. For glass and other dielectric media, when î =

    Brewster inciding angle (qB)

          reflexion of parallel component is none (=>

    polarized light

          that vibrates only in the plane perpendicular to the inciding one) and the reflexed and refracted rays are perpendicular between them (

    qB

          + ê = 90°) => n

    1.

          sen

    qB

          = n

    2.

          sen (90 -

    qB

          ) = n

    2.

          cos

    qB

          =>

    qB = arctg (n2,1)

          Sign conventions :

          • + marks real, R region (space-object region), and right images
          • - marks virtual, V region (space-image region), and virtual images

    Virtual image

          : locus of coming point of prolongements of a bundle of divergent reflexed rays. It cannot be collected on a display but just sensed if the eye is located along the route of the divergent bundle.

    Lens

          : a transparent optic system consisting of 2 diopters (of which at least one curved) that creates a real or virtual image of an object or of an image produced by another optic system

          • spherical lenses
            • convergent spherical lenses are used to correct hypermetropia
              • biconvex (A)
              • planoconvex (C)
              • concavoconvex, periscopic convex, converging meniscus (E)
            • divergent spherical lenses are used to correct myopia
              • biconcave (B)
              • planoconcave (D)
              • convexoconcave, periscopic concave, diverging meniscus (F)
          • They all have

    2 curvature centres

            joined by the

    principal optic axis

            (passing also for

    vertices

            ,

    optic centre

            (the only point that doesn’t deviate light rays) and

    2 focuses

            (

    p

            and

    q

            : the points where images of light sources placed on optic axis at infinite distance form)). Lenses are termed

    subtle

            when they approximate

    Gauss conditions

            : small aperture (angle from curvature centres), paraaxial incident rays falling on point near the optic axis, which thickness negligible with respect to curvature radii.

    Dioptric power

            = (n

    2

            - n

    1

            ) / R  [m

    -1

            or diopter (D)]. It has additive property (on the contrary of

    f

            ).

    Convergence or power of a lens (D)

            = 1 / f = (n

    1,2

            -1 ) (1/r – 1/r

    1

            ). A paraaxial ray is deviated by

    a

            ~ D. The image of a point placed at a distance p from optic centre forms at a distance q.

    Conjugate points formula

            : 1/p + 1/q = 1/

    f

            = 2/r => q = p

    .f

            / (p -

    f

            )

    Linear or longitudinal enlargement (Gl)

            =

    f

            / (p -

    f

            ) = q/p.

     

            Images can be constructed as intersections of 2 rays emerging from the lens : the rays parallel to the optic axis, passing by the extremities of the object or the optic centres are chosen.

    Divergent lenses

            (as convex mirrors) have

    f

            < 0 (a.k.a.

    negative lenses

            ) and always form virtual, right images with G

    l

            < 1.

    Convergent or positive lenses

            (as concave mirrors) have

    f

            > 0 (a.k.a.

    positive lenses

            ) :

            • if p < r => reduced, real and viceversed images form, with f < q < r (limit case : if p = r => q = r)
            • if f < p < r => enlarged, real, and viceversed images form, with q > r (limit case : if p = f => q = infinite)
            • if 0 < p < f => enlarged, virtual, right images form, on the same side of the object)
          • cylindric lenses are used to correct astigmatism
            • planoconvex (H)
            • planoconcave (G)
            • biconvex
          • toric lenses
            • planoconvex
            • planoconcave
          • a lens resembling an octopus eye is made up of a sphere that consists of hundreds of thousands of layers of plastic and could revolutionize cameras, telescopes and spectacles. Traditional glass lenses use a curved surface to focus incoming light towards a central point. The stronger the lens, the more curved its surface must be and therefore the thicker and heavier it is. In nature, eyes avoid this problem by using materials whose density varies in a certain way. Light is bent, or refracted, when it travels between 2 substances that have different densities (or refractive indices), such as air and water. The greater the difference between the 2 materials, the more the light is refracted. So a flat object that has a greater refractive index towards its edges can focus light like a curved lens. Many biological lenses consist of up to hundreds of thousands of nanolayers, each of which has a slightly different refractive index. The layers form a smooth density gradient that helps to focus light. In human eyes, this lens is made up of about 22,000 layers. But animals that live in water, which has a high refractive index compared with air, need stronger lenses. The octopus eye, for example, can focus light 5 times more strongly than a human eye. Plastic films that were 50 mm thick and consisted of roughly 6,000 nanolayers of 2 different polymers, either poly(methylmethacrylate) (PMMA) or poly(styreneacrylonitrile), have different refractive indices, so by varying the number of polymer nanolayers in each film, the researchers created 100 films, each of which had a refractive index that differed from the next by 1%. When stacked and formed into a sphere, the films created an eye with a focusing ability equivalent to that of the octopus eye. As the technique is developed, they will be able to create even more powerful lenses. It’s possible to create almost any refractive index. There are several practical advantages to this type of lens: glass lenses of a comparable strength would weigh almost 4 times as much. And a polymer lens is more flexible: the focus can be tweaked just by altering a few of the nanolayers. Eventually the researchers plan to use a softer plastic that will make it easy to shift the focus of the lens by simply squeezing it. Future applications include lightweight lenses that can be focused remotely. These could be used for unmanned aerial vehicles and missile guidance, which will please the research project’s sponsor, the Defense Advanced Research Projects Agency. But the technology could also benefit human vision. Baer has already used his nanolayers to make himself a pair of glasses; they meet his prescription, despite being absolutely flat.
        • magnetic field strength
          • 1 Gauss (G) = 1 line of flux per cm2. The strength of the earth’s magnetic field at its surface is about 0.5 to 1 G, but as larger magnetic fields have become commonplace, the unit gauss (G) has been largely replaced by the more practical unit …
          • 1 Tesla (T) = 1 W/m2 = 10,000 G, where 1 Weber represents 108 flux lines.
        • relative hardness of a material
          • Knoop hardness number : calculated from the load employed and the length of the long axis of the impression made by the rhomboidal pyramid of a diamond pressed into the surface of the material being tested. It is the test most commonly used in dental practice to test the hardness of teeth.
          • Brinell hardness number : calculated after measuring the diameter of the impression made by a steel ball pressed under a known load into the surface of the material being tested; equal to the load in kilograms divided by the surface area of the indentation in square millimeters.
          • Rockwell hardness number : determined by measuring the depth of the impression made by a steel or diamond penetrator pressed into the surface of the material being tested. There are a number of Rockwell hardness tests and scales, using various combinations of loads and penetrators; the load and penetrator combination must always be specified when stating a Rockwell hardness number.
          • Vickers hardness number / diamond pyramid hardness : determined by measuring the long diagonals of indentation made by pressing the pyramidal point of a diamond into the surface of the material being tested; equal to the load in kilograms divided by the area, in square millimeters, of the recovered indentation
      • Some quantitative considerations on biological systems
        • spherical cells : surface area / volume = 3/r
        • cubic aggregates (e.g. : sarcinae) : surface area / volume = 6/l
      • The Virtual Library – Physiology and Biophysics

     

      • Interactions :
        • bimolecular reaction [A] + [B] <=> [AB]
          • kinetics of the reaction
            • on rate = k+1 [A] [B], where k+1 [M-1s-1]
            • off rate = k-1 [AB], where k-1 [s-1]
          • at the equilibrium k+1 [A] [B] = k-1 [AB]
            • k+1 / k-1 = Ka = [AB] / [A] [B] = association or equilibrium constant [M-1]. Antibodies with high affinity have .
            • k-1 / k+1 = Kd = [A] [B] / [AB] = dissociation constant [M]
          • The reason why K

    d

            is often determined in preference to K

    a

            , is that determination of K

    a

            requires the reaction to proceed to equilibrium, whereas K

    d

            can be derived from reactions in which half the concentration of antigen is complexed with the antibody. Thus [A] = [AB] and K

    d

            = [B]. Antibodies with high affinity have K

    a

            > 10

    7

            M

    -1

            and K

    d

            < 10

    -7

            M. Different reactions can have identical K

    a

            but different rate constants. k

    +1

            can vary over the range from 10

    5

            to 10

    8

            M

    -1

            s

    -1

            . k

    -1

            ranges from 1 to > 10

    3

            s

    -1

            . As the off rate depends on the concentration of only one species ([AB]), there is a very simple relation between it and the time (in seconds) taken for the complex to dissociate to 50%: t

    1/2

            = -ln0.5 / k

    -1

            .
        • at equilibrium the binding of a multivalent antibody
          • univalent ligand may be expressed as :
              K

    a

              = r / (valence – r) [Ag]

    free

            where r = average number of Ag molecules bound per Ab molecule.

     

            A set of values of r and [Ag]

    free

            can be obtained from a series of experiments in which the concentration of antibody is kept constant and from these a plot (Scatchard plot) can be constructed in which

    r/c is plotted against r

            .

            • linear plot => monoclonal antibodies.
            • nonlinear plot => polyclonal antibodies

            At saturation ([Ag]

    free

            very high) the limiting value of r is 2 for IgG and 10 (instead of the usual 5) for IgM.

          • multivalent ligand depends on the distance between epitopes

          Binding :

          • monogamous binding : 1 multivalent antibody binds 2 identical epitopes on a same multivalent antigen
          • bigamous binding : 1 multivalent antibody binds 2 identical epitopes on 2 different particles

          The term

    avidity

        is often used to indicate the overall ability of antibodies to interact with antigen. The term has practical value but does not define precisely the contribution of affinity vs valency vs epitope density to antibody-antigen binding. It merely describes the net result of the combination of these factors to antigen binding.
    • Web resources