# Atomic structure part 2/3

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14-Jan-2017Category

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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: = 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:

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

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: 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 !

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