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Chapter 1 - Basic Concepts - atoms

1 Chapter 1 - Basic Concepts : atomsDiscovery of atomic structureJJ Thomson (1897) Milliken (1909)Rutherford (1910)Rutherford (1911)2 Symbol p+ e-n0 Mass (amu) 1919, Rutherford 1897, Thomson 1932, ChadwickAtomic and Mass Numbers126 CSymbolMass numberAtomic number (optional)Atomic number (Z): equal to the number of protons in the nucleus. All atoms of the same element have the same number of protons. Mass number (A): equal to the sum of the number of protons and neutrons for an mass unit (amu) is 1/12 the mass of 12C ( 10-27kg)AZE3 Isotopes of HydrogenHydrogen1 proton1 electronDeuterium1 proton1 neutron1 electronTritium1 proton2 neutrons1 electron+++The atomic massis the weighted average mass, of the naturally occurring element. It is calculated from the isotopes of an element weighted by their relative abundances.

13 Spin Quantum Number, ms •Spin angular number, s, determines the magnitude of the spin angular momentum of a electron and has a value of ½. •Since angular momentum

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Transcription of Chapter 1 - Basic Concepts - atoms

1 1 Chapter 1 - Basic Concepts : atomsDiscovery of atomic structureJJ Thomson (1897) Milliken (1909)Rutherford (1910)Rutherford (1911)2 Symbol p+ e-n0 Mass (amu) 1919, Rutherford 1897, Thomson 1932, ChadwickAtomic and Mass Numbers126 CSymbolMass numberAtomic number (optional)Atomic number (Z): equal to the number of protons in the nucleus. All atoms of the same element have the same number of protons. Mass number (A): equal to the sum of the number of protons and neutrons for an mass unit (amu) is 1/12 the mass of 12C ( 10-27kg)AZE3 Isotopes of HydrogenHydrogen1 proton1 electronDeuterium1 proton1 neutron1 electronTritium1 proton2 neutrons1 electron+++The atomic massis the weighted average mass, of the naturally occurring element. It is calculated from the isotopes of an element weighted by their relative abundances.

2 Atomic mass = fractionAmA+ fractionBmB+ ..RuS84 Allotropeselement's atoms are bonded together in a different manner Successes in early quantum theoryE= h c= 5 22'111nnR where R is the Rydberg constant for H, 105cm-1 =hmvwhere his Planck s constant, 10-34 Js( x) ( mv) h4 Uncertainty PrincipleWave Nature of Matter6 Schr dinger wave equationThe probability of finding an electron at a given point in space is determined from the function 2where is the )(82222 VEhmdxdwhere m= mass, E= total energy, and V= potential energy of the particle1d3d0)(822222222 VEhmzyxwhere m= mass, E= total energy, and V= potential energy of the particleIt is convenient to use spherical polar coordinates, with radial and angular parts of the wavefunction.),()(),()(),,( ArRrzyxangularradialCartesian Definition of the polar coordinates (r, , ) The wave function is a solution of the Schrodinger equation and describes the behavior of an electron in a region of space called the atomic orbital.

3 We can find energy values that are associated with particular wavefunctions. Quantizationof energy levels arises naturally from the Schrodinger Orbitaln l mlRadial part of the wavefunction, R(r) angular part of the wavefunction, A( , )1s1 0 02s2 0 02px2 1 +12pz2 1 02py2 1 -1re 22/)2(221rer 2/621rre 2/621rre 2/621rre 21 21 2)cos(sin3 2)(cos3 2)sin(sin3 Atomic OrbitalsA wavefunction is a mathematical function that contains detailed information about the behavior of an electron. An atomic wavefunction consists of a radial component R(r), and an angular component A( , ). The region of space defined by a wavefunction is called an atomic orbitals possess the same the principle quantum numberlis the orbital, angular momentum , or azimuthal quantum numberml is the magnetic quantum numbermsis the spin quantum number81s2sPlot of the radialpart of the wavefunction against distance (r) from the nucleus(n-l-1) radial nodesnsorbitals have (n-1 radial nodes), nporbitals have (n-2 radial nodes), ndorbitals have (n-3 radial nodes), nforbitals have (n-4 radial nodes).

4 Plots of radial parts of the wavefunctionR(r) against rfor the 2p, 3p, 4pand 3datomic orbitals9 Radial Distribution Function, 4 r2R(r)2 1* d 12 dRadial distribution functions, 4 r2R(r)2, for the 3s, 3pand 3datomic orbitals of the hydrogen atom10 Boundary surfaces for angular part of wavefunction, A( , )Different colors of lobes are significant For s orbital it has constant phase the amplitude of the wavefunction has a constant sign For a p orbital, there is one phase change with respect to the boundary surface. This phase change occurs at a nodal of an sand a set of three degenerate patomic through the (a) 1s(no radial nodes), (b) 2s(one radial node), (c) 3s(two radial nodes), (d) 2p(no radial nodes) and (e) 3p(one radial node) atomic orbitals of hydrogen. Radial probability functionsProbability density12set of five degenerate datomic orbitalsOrbitals energies in hydrogen-like species22nkZE k = 103kJ mol-1Z = atomic numberEn =3n =2n =1shell3s2s1s3p2p3dIn the absence of an electric or magnetic field these atomic orbital energy levels are degenerate; that is they are identical in Quantum Number, ms Spin angular number, s, determines the magnitudeof the spin angular momentum of a electron and has a value of.

5 Since angular momentum is a vector quantity, it must have direction Magnetic spin quantum number, ms, can have values +1/2 or -1 orbital is fully occupied when it contains two electrons which are spin paired; one electron has a value of ms= +1/2 and the other -1/2ml= 2 +2(h/2 )ml= 1 +(h/2 )ml= 0 0ml= -1 -(h/2 ))2/(6 h)2/(6 h)2/(6 h)2/(6 h)2/(6 hml= -2 -2(h/2 )Resultant angular momentumResultant magnetic momentAngular momentum , the inner quantum number, j, spin-orbit couplingz component of orbital angular momentumorbital angular momentum141H ground stateMany-electron atomGround State Electronic ConfigurationsThe sequence that approximately describes the relative energies or orbitals in neutralatoms:1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p< 5s < 4d < 5p < 6s <5d 4f < 6p < 7s < 6d 5f 15 Penetration and shieldingRadial distribution functions, 4 r2 R(r)2, for the 1s, 2sand 2patomic orbitals of nuclear chargeZeff= Z SSlater's Rules for Calculating Shielding1.

6 Write out electron configuration of the element [1s][2s,2p][3s,3p][3d][4s,4p][4d][4f] [5s,5p] etc*2. Electrons in an group higher in this sequence contribute nothing to For an electron in nsor nporbitali. Each of the other electrons of same groupcontributes S= each (except in 1s, S= )ii. Each electron in (n 1) shell, contributes S= Each electron in (n 2) or lower shell, contributes S= For an electron in an ndor nfgroupi. Each of the other electrons of same ndor nf groupcontributes S= each ii. Each electron in a lower group, contributes S= *A bracket indicates a group and nis the principle quantum number of a shell17 The aufbau principle Orbitals are filled in the order of energy, the lowest energy orbitals being filled first. Hund sfirst rule: in a set of degenerate orbitals, electrons may not be spin paired in an orbital until each orbital in the set contains one electron; electrons singly occupying orbitals in a degenerate set have parallel spins, have the same values of ms.

7 Pauli Exclusion Principle : no two electrons in the same atom can have identical sets of quantum numbers n, l, ml, ms;each orbital can accommodate a maximum of two electrons with different and core electronsIonization Energy19 Ionization EnergyElectron AffinityElectron affinityis defined as minus the change in internal energy for the gain of an electron by a gaseous atom. EA = - U(0K)


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