Atomic structure part 2/3

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  • Atomic Structure Part 2 Quantum Numbers

    Electron Configuration


    UP Aug.2016

  • What we will learn part 2:

  • Review Lesson 1 Atomic nucleus

    atomic mass unit amu

    Isotopes / MS

    Bohr model of the Hydrogen atom absorption and emission spectra energy levels in the atom = orbits

    Electron as standing wave deBroglie: = h/p = h/(mv)

    Wavefunction for electrons in a box leading to:

    Schroedinger equation (Energy of electron waves)

  • Emission spectra with single lines for each element => electrons must be on fixed orbits (n)

    Each line with a wavelength corresponds to an electron transition with an energy E = E2 E1 = h * c / 1/ = wavenumber in cm-1

  • Energy unit electronVolt eV = energy of 1 electron in a field of 1 V

    1 eV => = 1240 nm = 1240 nm / E [eV]

  • Check

    Which light will an electron emit, when it falls from energy level 4 to 2 ? (is it shorter or longer than from 4 to 3 ?)

    Which energy in eV will an electron bring from its ground level to the first excited state ?

  • Describe the wavefunction and its energy

    The function can be described as:

    From this we find:

    The kinetic energy is: -> Schroedinger equation for 1 dimension:

    ( is fixed with = 2L)

  • Describe the wavefunction


  • From this we remember....

    The Schroedinger equation describes the energy of waves (not just electrons, but all particles and also vibrations)

    This energy is proportional to the curvature of the wave (which is the second derivative of the wave function )

    The energy of an orbit n becomes n2 for the next orbit (or: the energy of the orbits increases quadratic)

    The wavefunction 2 (squared) describes the probability to find a particle in a certain space x

  • Summary Summary

  • Uncertainty principle (Heisenberg 1927)

    A further conclusion from the particle in the box model is that the location of a small particle is related to its momentum p the Heisenberg equation:

  • Demo for the H-Atom model

    The whole story (29 mins):

    Start Clip

    Quantum Mechanics_ The Uncertainty Principle.mp4

  • Particle in the box - example

    We can apply the idea on the ionization energy for a C-atom:

    h = 6.63 * 10-34 kg m2/ s2

    me = 9.11 * 10-31 kg

    1 J = 6.24 * 1018 eV

    J eV =

  • From line spectra to wavefunctions (orbitals)

    Model the electron as a standing wave in 3D, we can describe the most likely places of an electron and its energy from the Schroedinger Equation

    If you want to know this in detail: and:

    This equation leads to 3 quantum numbers which describe the energy and the distribution of the electron in an atom

  • Quantum Numbers When we extend the model of the particle in a box to 3 dimensions we have to use 3 quantum numbers:

  • 3 quantum numbers in spherical coordinates

    n: main quantum number (start with 1)

    l : angular ( 0,1 .. n-1)

    m: magnetic ( -l 0 +l )

    Electrons can live only in these orbitals (spaces) defined by 3 quantum numbers

    Up to 2 electrons can exist in one orbital

  • Observation of quantum numbers in line spectra

  • Main spectral lines = n

    Fine structure = l

    With magnetic field: Zeeman effect magnetic quantum no. m

  • Questions

    How many orbitals are possible for the energy level n = 2 and how many electrons can live there maximum ?

    n = 2 l = 0 and 1 (s and p level) m = 0 and -1, 0, +1 (px, y and z)

  • Part 2:

  • The order of energy changes at Ca Sc !