Adobe Systems Department of Biophysics, Medical Faculty, Masaryk University in Brno 1 Lectures on Medical Biophysics Structure of matter Electron diffraction pattern curie Marie Skłodowska Curie (1867 – 1934) and Pierre Curie (1859 – 1906) Adobe Systems 2 Matter and Energy ØEverything is made up of basic particles of matter and fields of energy / force, which also means that the fundamental structural elements of the organic and inorganic world are identical. ØLiving matter differs from non-living matter mainly by its much higher level of organisation. Adobe Systems 3 Elementary Particles of Matter (i.e. having - probably - no internal structure) Ø„force“ particles – integer spin – bosons ØVector bosons – spin 1 ØFoton (EMR) ØGluons (Strong) ØW+, W-, Z0 (Weak) ØGraviton ?? ØScalar boson – spin 0 ØHiggs boson Ø„matter“ particles – noninteger (odd) spin - fermions ØThe elementary particles of matter are leptons and quarks ØLeptons – electron, muon, Tauon, neutrinos and their anti-particles –particles without internal structure? ØQuarks (u, c, t, d, s, b) – particles without internal structure Ø ØComposite particles ØHadrons – heavy particles formed of quarks - baryons (fermions - proton (u, u, d), neutron (d, d, u)) mezons (bosons (quark-antiquark)) Ø [USEMAP] 4 The Four Fundamental Energy / Force Fields gravitational ? [USEMAP] electromagnetic strong weak Adobe Systems 5 Photons ØPhotons - energy quanta of electromagnetic field, zero (rest) mass ØEnergy of (one) photon: E = hf = hc/l h is the Planck constant (6.62·10-34 J·s), f is the frequency, c is speed of light in vacuum, l is the wavelength. Adobe Systems 6 Particles and Field Energy Quanta Particles of matter and field energy quanta are capable of mutual transformation (e.g., an electron and positron transform to two gamma photons in the so-called annihilation – this is used in PET imaging). 7 Electron diffraction pattern Quantum Mechanics The behaviors of ensembles of a given type of particle obey equations which are similar to wave equations. (http://www.matter.org.uk/diffraction/electron/electron_diffraction.htm) On the left pattern formed on a photographic plate by an ensemble of electrons hitting a crystal lattice. Notice that it is very similar to the diffraction pattern produced by a light wave passed through optical grating. 8 kag10602_e kag10601_e Quantum Mechanics tunnel effect: kag10602_e kag10601_e Adobe Systems 9 Quantum Mechanics: Heisenberg uncertainty relations dr·dp ≥ h/4p dE·dt ≥ h/4p The position r and momentum p of a particle cannot be simultaneously measured with independent precision (if the uncertainty of particle position – dr – is made smaller, the uncertainty of particle momentum – dp – automatically increases). The same holds for the simultaneous measurement of energy change dE and the time dt necessary for this change. h is the Planck constant. 10 Schrödinger equation (to admire J) „one-dimensional“ S. equation Radial co-ordinates of an electron in a hydrogen atom Y - wave function S. equation for the electron in the hydrogen atom according http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html Obsah obrázku hodiny Popis byl vytvořen automaticky Adobe Systems 11 Solution of the Schrödinger Equation ØThe solution of the Schrödinger equation for the electron in the hydrogen atom leads to the values of the energies of the orbital electron. ØThe solution of the Schrödinger equation often leads to numerical coefficients which determine the possible values of energy. These numerical coefficients are called quantum numbers Adobe Systems 12 Quantum numbers for Hydrogen ØPrincipal n = 1, 2, 3 …. (K, L, M, ….) ØOrbital for each n l = 0, 1, 2, …. n – 1 (s, p, d, f …) ØMagnetic for each l m = 0, ±1, ±2, …±l ØSpin magnetic for each m s = ±1/2 Ø ØPauli exclusion principle – in one atomic electron shell there cannot be present two or more electrons with the same set of quantum numbers. 13 Ionisation of Atoms • • • • • • Example of ionisation: photoelectric effect h·f = Eb + ½ m··v2 The binding energy of an electron Eb is the energy that would be required to liberate the electron from its atom – depends mainly on the principal quantum number. Secondary electron Primary photon excitation ionisation Adobe Systems 14 Emission Spectra Dexcitations between discrete energy levels result in emitted photons with only certain discrete energies, i.e. radiation of certain frequencies/wavelengths. slits prism Hydrogen discharge tube Visible emission spectrum of hydrogen. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/bohr.html modro- = bluish Learn the Czech names of colours J Adobe Systems 15 Hydrogen spectrum again magenta, cyan and red line according http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/text_images/CH07/FG07_ 19.JPG Excitation of electrons Emission of light Adobe Systems 16 Excitation (absorption) Spectra for Atoms Absorption lines in visible spectrum of sun light. Wavelengths are given in Angströms (Å) = 0.1 nm http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/07.html Transitions between discrete energy states of atoms!! Adobe Systems 17 Excitation (Absorption) Spectrum for Molecules According: http://www.biochem.usyd.edu.au/~gareth/BCHM2001/pracposters/dyeZ.htm Absorption spectrum of a dye Wavelength 18 Atom nucleus Proton (atomic) number – Z Nucleon (mass) number – A Neutron number – N N = A - Z Atomic mass unit u = 1.66·10-27 kg, i.e. the 1/12 of the carbon C-12 atom mass Electric charge of the nucleus Q = Z x 1.602·10-19 C If relative mass of electron = 1 Þ Relative mass of proton = 1836 Þ Relative mass of neutron = 1839 fission 19 Mass defect of nucleus = measure of nucleus stability: dm = (Zmp + Nmn) - mnuc Sources: http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/text_images/CH19/FG19_ 05.JPG http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/text_images/CH19/FG19_ 06.JPG fission nucleon number nuclear synthesis scale change E = dm.c2 This formula allows to calculate amount of energy liberated during the synthesis of the nucleus. Adobe Systems 20 Nuclides Ønuclide - a nucleus with a given A, Z and energy ØIsotopes - nuclides with same Z but different A ØIsobars – nuclides with same A but different Z ØIsomers – nuclides with same Z and A, but different energy (e.g., Tc99m used in gamma camera imaging) Adobe Systems 21 Isotope composition of mercury % of Hg atoms vs. isotope nucleon number (A) According to: http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/text_images/CH07/FG07_ 08.JPG • • • • • A Nucleon number Adobe Systems 22 What else is necessary to know? ØRadionuclides – nuclides capable of radioactive decay ØNuclear spin: Nuclei have a property called spin. If the value of the spin is not zero the nuclei have a magnetic moment i.e, they behave like small magnets - NMR – nuclear magnetic resonance spectroscopy and magnetic resonance imaging (MRI) in radiology are based on this property. Adobe Systems 23 Author: Vojtěch Mornstein Content collaboration and language revision: Carmel J. Caruana Presentation design: Lucie Mornsteinová Last revision: Daniel Vlk october 2023 >