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Lecture 18

PHYS 242 Lecture 18: PHYS242_Lecture_18

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Queen's University
PHYS 242
Wolfgang Rau

56 ENPHPHYS 242 Fall 2014 L 18 2. Quantum Phenomena 2.1 Quantisation of Matter 2.1.1 Atoms and the statistical approach to physical phenomena Democritus who lived around 500 B.C. was the first of whom we know to have asked the question what would happen if one divided a piece of matter in half and again in half, and again, and again He advocated the idea that this should not be possible infinitely often but one would end with a smallest possible quantity of matter that would be indivisible, atomos in Greek. Aristotle who was very influential at the time dismissed this idea as worthless and so it disappeared for about 2000 years. th In modern times it reappears in the 17 century and found first substantial support through Robert Boyles discovery that the product of pressure and volume of a gas is constant if the temperature is constant. Newton explained in his Principa why this should be the case if one assumes that gas consisted of tiny hard particles. Combining Boyles Law with Charles Law (at constant pressure the volume of a given amount of gas is proportional to its temperature) leads to the Ideal Gas Law: constant . Further support for the atomistic theory of matter came from Proust, th Dalton and GayLussac (beginning of the 19 century). They explained the constant ratios of the involved elements when producing chemical compounds (stoichiometry). An important step was done by Avogadro in 1811 when he put down a set of hypotheses: Gas consists of particles that are small compared to their distance. Equal volumes of gas consist of the same number of particles (given and are the same), independent of the type of gas. For certain chemical elements the gas particles consist of molecules built out of 2 (or more) atoms With the second of these hypotheses we can rewrite the Ideal Gas Law with the number of particles and a certain constant (Boltzmann constant, 1.381 10 JK 8.617 10 eV K): (46) In 1865 Loschmidt was the first to find a way to determine the number of particles per volume based on the kinetic gas theory developed by Clausius, Maxwell and others. This number is called Loschmidt Number or more often Avogadros Number and is usually given in terms of moleculesmol: 6.022 10 molecules mol where 1 mol 1 g 1 amu and 1 amu atomic mass unit of the mass of aCatom or 931 MeV . W. Rau
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