Atomic structure part 2/3
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The document provides an overview of atomic structure focusing on quantum numbers, electron configuration, and the Schrödinger equation. It explains the relationship between energy levels, electron transitions, and how electrons are represented as standing waves, using the particle-in-a-box model. Additionally, it introduces key concepts such as the uncertainty principle and the quantum numbers defining electron orbitals in an atom.
![Energy unit “electronVolt” eV
= energy of 1 electron in a field of 1 V
1 eV => λ = 1240 nm
λ = 1240 nm / E [eV]](https://image.slidesharecdn.com/atomicstructurepart2-160827060128/85/Atomic-structure-part-2-3-5-320.jpg)
Atomic structure part 2/3
- 1. Atomic Structure Part 2 Quantum Numbers Electron Configuration Dr.Chris UP Aug.2016
- 2. What we will learn … part 2:
- 3. 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: λ = h/p = h/(mv) • Wavefunction for electrons in a “box” leading to: • Schroedinger equation (Energy of electron waves)
- 4. Emission spectra with single lines for each element => electrons must be on fixed orbits (n) Each line with a wavelength λ corresponds to an electron transition with an energy ∆E = E2 – E1 = h * c / λ 1/ λ = ν wavenumber in cm-1
- 5. Energy unit “electronVolt” eV = energy of 1 electron in a field of 1 V 1 eV => λ = 1240 nm λ = 1240 nm / E [eV]
- 6. 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 ?
- 7. 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: http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_6/node1.html ( is fixed with = 2L)
- 10. 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
- 11. SummarySummary
- 12. 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: http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html#c2
- 13. Demo for the H-Atom model http://www.youtube.com/watch?v=Fw6dI7cguCg The whole story (29 mins): http://www.youtube.com/watch?v=xrz_-l2akFA Start Clip
- 14. 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=
- 15. 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: http://www.youtube.com/watch?v=7LBPXP09KC4 and: http://www.physicsforidiots.com/quantum.html • This equation leads to 3 quantum numbers which describe the energy and the distribution of the electron in an atom
- 16. Quantum Numbers When we extend the model of the particle in a box to 3 dimensions we have to use 3 quantum numbers:
- 17. 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
- 18. “Observation” of quantum numbers in line spectra
- 19. • Main spectral lines = n • Fine structure = l • With magnetic field: Zeeman effect magnetic quantum no. m
- 20. 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)
- 22. Part 2:
- 23. The order of energy changes at Ca – Sc !