Atomic structure part 2/3

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Atomic Structure Part 2 Quantum Numbers Electron Configuration Dr.Chris UP Aug.2016

Transcript of Atomic structure part 2/3

Page 1: Atomic structure part 2/3

Atomic Structure Part 2 Quantum Numbers

Electron Configuration

Dr.Chris

UP Aug.2016

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What we will learn … part 2:

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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)

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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

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

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

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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 ?

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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)

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Describe the wavefunction

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html

normalization

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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

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Summary Summary

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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

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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

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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 =

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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

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

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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

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“Observation” of quantum numbers in line spectra

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• Main spectral lines = n

• Fine structure = l

• With magnetic field: Zeeman effect magnetic quantum no. m

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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)

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Part 2:

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The order of energy changes at Ca – Sc !