Atomic structure part 2/3
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Transcript of Atomic structure part 2/3
Atomic Structure Part 2 Quantum Numbers
Electron Configuration
Dr.Chris
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: λ = 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 λ corresponds to an electron transition with an energy ∆E = E2 – E1 = h * c / λ 1/ λ = ν wavenumber in cm-1
Energy unit “electronVolt” eV = energy of 1 electron in a field of 1 V
1 eV => λ = 1240 nm λ = 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:
http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_6/node1.html
( is fixed with = 2L)
Describe the wavefunction
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html
normalization
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:
http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html#c2
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
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: 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
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 !