Bez názvu1 kopie 1 Lectures on Medical Biophysics Department of Biophysics, Medical Faculty, Masaryk University in Brno mush revlight5b Electron diffraction pattern Bez názvu1 kopie 2 Structure of matter curie http://www.accessexcellence.org/AE/AEC/CC/historical_background.html Lectures on Medical Biophysics Department of Biophysics, Medical Faculty, Masaryk University in Brno logo Masarykova univerzita – Lékařská fakulta Marie Skłodowska Curie (1867 – 1934) and Pierre Curie (1859 – 1906) Bez názvu1 kopie 3 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. • Bez názvu1 kopie 4 Elementary Particles of Matter ØThe elementary (i.e. having no internal structure) particles of matter are leptons and quarks • ØLeptons – electrons, muons, neutrinos and their anti-particles – light particles without internal structure • ØQuarks (u, c, t, d, s, b) – heavier particles without internal structure • ØHadrons – heavy particles formed of quarks e.g., proton (u, u, d), neutron (d, d, u) Ø Bez názvu1 kopie [USEMAP] 5 The Four Fundamental Energy / Force Fields gravitational electromagnetic strong weak Strong : weak : electromagnetic : gravitational force - 1 : 10-5 : 10-2 : 10-39 at interaction distance of about 10-24 m; 10-7 : ~0 : 10-9 : 10-46 at a distance of about 10-18 m (1/1000 of atom nucleus dimension). In the distance equal to nucleus dimension goes to zero also strong interaction. Bez názvu1 kopie 6 Photons ØPhotons - energy quanta of electromagnetic field, zero 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 vakuum, –l is the wavelength. Bez názvu1 kopie 7 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) Bez názvu1 kopie 8 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. Bez názvu1 kopie 9 kag10602_e kag10601_e Quantum Mechanics tunnel effect: kag10602_e kag10601_e Bez názvu1 kopie 10 Quantum Mechanics: Heisenberg uncertainty relations •dr·dp ≥ h/2p •dE·dt ≥ h/2p • •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. Bez názvu1 kopie 11 Schrödinger equation (to admire) „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 Bez názvu1 kopie 12 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 Bez názvu1 kopie 13 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. Bez názvu1 kopie 14 Ionisation of Atoms • • • • • • Example of ionisation: photoelectric effect hf = Eb + ½ mv2 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 Bez názvu1 kopie 15 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 Bez názvu1 kopie 16 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 Bez názvu1 kopie 17 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!! Bez názvu1 kopie 18 Excitation (Absorption) Spectrum for Molecules According: http://www.biochem.usyd.edu.au/~gareth/BCHM2001/pracposters/dyeZ.htm Absorption spectrum of a dye Wavelength Bez názvu1 kopie 19 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 = Z1.602·10-19 C If relative mass of electron = 1 Þ Relative mass of proton = 1836 Þ Relative mass of neutron = 1839 Bez názvu1 kopie 20 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. Bez názvu1 kopie 21 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) Bez názvu1 kopie 22 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 Bez názvu1 kopie 23 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. Bez názvu1 kopie 24 Author: Vojtěch Mornstein Content collaboration and language revision: Carmel J. Caruana Presentation design: Lucie Mornsteinová Last revision:December 2018 Author: Vojtěch Mornstein Content collaboration and language revision: Carmel J. Caruana Presentation design: Lucie Mornsteinová Last revision:December 2018