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1.2 The mass of the atom With the methods of chemistry: • Dalton’s law of constant and multiple proportions The atomic weights are approximately whole-number multiples of the atomic mass of the Hydrogen atom. The atomic mass unit 1 u or 1 amu is defined as the mass of Hydrogen The relative atomic masses: Arel(N)14, Arel(O)16 1961 standard: 1 u = 1/12 of the mass of 12C To be expedient for the experimental precision determination of atomic masses by chemical means Compare: amu(H) : amu(12C) = 0.99996 : 1.00000 Avogadro’s hypothesis: equal volumes of gas (at similar conditions: pressure, temperature) contain the same number of molecules or atoms. Avogadro’s number NA: 1 mole of any substance contains the same number (NA) of atoms. The present value: NA = (6.022045 ± 0.000005) × 1023 mole-1 The absolute atomic mass: Matom = mass of 1 mole of the substance / NA 1 mole of 12C is 12 grams: m(126C ) 12 g / mol 19.92516 10 27 kg NA m(O) 26.5584 1027 kg 1 u = (12/12) grams / NA = (1.660565 ± 0.000005) × 10-27 kg = 931.478 MeV/c2 Determination of Avogadro’s number NA • Electrolysis In electrolytic decomposition of salts from a solution, for 1 mole of a monovalent substance (for example Cu+), a charge of 96485 As (Ampere-second) can be required. NA = F/e, F: the Faraday constant, 96485 As/mole e: the charge of a single electron Other methods to determine the mass of atom: • The gas constant R and Boltzmann’s constant k, k = R/NA • X-ray diffraction in Crystals • Determination using radioactive Decay • Mass spectroscopy Mass spectroscopy — a physical method: By determining the ratio of charge to mass e/m, by the deflection of ionized atoms moving through electronic and magnetic fields. The oldest and most easily understandable – Parabola method by Thomson in 1913 Parabola method oven The ion beam, collimated by the slit S, is deflected by the magnet M and the condenser C in the x and y directions. Separation of a mixture of hydrocarbon. The orbit of deflected particles on screen: y 2E m 2 x 2 2 l B e Advantage of the Parabola method: differing velocities due to their preparation in an oven, those ions having the same value of e/m on a same parabola Improved types (higher resolution) and modern applications: a) with velocity focussing (by Aston 1919) b) With directional focussing in a magnetic sector field by Dempster in 1918 c) Double focussing – velocity and directional focussing d) Quadrupole mass spectroscopy Quadrupole mass spectrometer Schematic of a quadrupole mass filter. The ion beam, moving in the +z direction, is deflected by a high-frequency alternating potential. In order for the beam to pass through the filter, a certain relation between e/m, the frequency , and the deflection voltages U and V must be fulfilled. The dashed orbit applies to an ion for which this condition is not met. 1.3 the size of the atom Methods in history: Application of the kinetic theory of gases Using ideal-gas law: pV = nRT Determining the atom size from the covolume of the Van der Waals equation in a real gas states: (p+a/V2)(V-b) = RT The interaction cross-section Mordern methods: Directly measured by Scanning Tunneling Microscopy (STM), and electron microscopy (SEM or TEM) X-ray diffraction measurement on crystals Incident X-rays 1 Diffracted x-rays 2 atoms Incident X-rays Atomic planes 1 2 Diffracted x-rays Bragg (in 1913) interference condition: 1= 2 = With the X-ray path difference: = AB+BC-AE = n 2dsin = n Practical methods of observing X-ray diffraction: • The Laue method: uses a single crystal, and polychromatic X-ray • The Bragg rotating crystal method: uses a single crystal with rotating angle, and a monochromatic X-ray • The Debye-sherrer method: uses a polycrystalline or powered sample, and a monochromatic X-ray 1.4 The periodic table The periodic system of the elements —— An ordering of the elements according to periodically recurring chemical and physical properties. • The periodically repeated chemical properties: the monovalence of the alkali atoms: 3Li, 11Na, 19K, 37Rb, 55Cs, 87Fr and the lack of reactivity of the rare gases: 2He, 10Ne, 18Ar, 36Kr, 54Xe, 86Rn • The periodically repeated physical properties: the atomic volumes and the ionisation energies The periodic system of the elements Atomic volumes and ionisation energies as function of the position in the periodic system of the elements. Particularly noticeable are the (relatively) large atomic volumes of the alkali metal atoms and the large ionisation energies of the noble gas atoms. The empirical regularities indicate corresponding regularities in the atomic structure –– table of periodic system of the element. The periodic table of the elements was first proposed in 1869 by Medeleev and Lothar Meyer. It is constructed by listing the atoms (elements) according to increasing the nuclear charge number Z. 1.5 Isotope The relative atomic masses Arel (by chemical method): near integer Mass number A: the hypothesis of Prout (in 1815), all atoms are made up of H atoms. A and Arel are nearly equal at many cases, but for Chlorine (17Cl), Arel = 35.5, for 38Sr, Arel = 87.62 With the aid of mass spectroscopy, Aston in 1920, the composition of naturally occuring Neon (10Ne) with the mass number A = 20, 21 and 22 Isotopes: atoms with the same nuclear charge number Z and differing mass numbers A Many elements consist of several isotopes Isotopes abundance the relative atomic mass Arel 20 90.92% 19.99244 10 Ne 21 0.26% 20.99385 10 Ne 22 8.82% 21.99138 10 Ne average Arel = 20.18 35 75.4% 17 Cl 37 24.6% 17 Cl average Arel = 35.457 1 99.986% 1H 2 0.014% 1H 3 (Deuterium, not natural) 1H average Arel = 1.008 Elements with only one stable isotope: 9 4 Be 27 13 Al 127 53 I Isotope separation —— a problem of technology and nuclear physics Separation of isotopes of 1 2 H 1 and 1 H , relatively easy, 238 235 and is more difficult. U 92 U 92 Methods of isotope separation (from economics and the state of technology) a) Electromagnetic separation : expensive and slow 1mg per hour at a current of 10-4 A, to separate 35g Cl, it needs 30 years b) By means of diffusion in a gas: 2 2 v1 / v2 m2 / m1 , since m1v1 m2 v2 c) The gas centrifuge: heavier isotope is acted upon by a stronger centrifugal force d) Thermodiffusion in a separation tube: temperature gradient in a mixture of gases e) Fractional distillation: heavier isotope in general has the higher boiling point f) Electrolysis molecules with heavier isotope are less easily decomposed than those with the lighter isotope g) Chemical reactions molecules with differing isotopic compositions react with different rates. h) Laser photochemistry for certain isotopes using photochemical reactions. Homework: Pp36, problems 3.2, 3.3