Bohrs model failed

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Bohrs model failed

• For atoms other than Hydrogen Bohrs theory
  failed and Bohr new this himself as in physics
• A charged body (ie. an electron) following a
  circular orbit will emit energy and as energy
  decreases so does the distance to the nucleus.
  Thus as the electron orbits it will get closer
  and closer to the nucleus and the atom will
  eventually collapse.

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Next comes Schrodinger

• Electrons moving around the nucleus can be
  thought of as forming standing waves which can be
  described by the de Broglie equation.
• Standing waves do not travel because they have
  fixed start and end points. Thus, they must
  contain a fixed number of half wavelengths.

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Schrodinger

• Thus only certain circularly shaped standing
  waves with a whole number of half wavelengths
  would be possible without destructive
  interference at the ends.
• These standing wave orbits (of sorts) would then
  only be possible at fixed distances from the
  nucleus thus supporting the energy quantization
  observation.

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At the same timeHeisenberg

• Heisenberg uncertainty principle
• There is a fundamental limitation to just how
  precisely we can know both the position and
  momentum of a particle at a given time. In
  laymans terms The more precisely we know a
  particles position the less we know about its
  momentum and vice versa.

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Schrodinger Heisenberg Orbitals

• Regardless of the method used to arrive at the
  theory of orbitals (either schrodingers or
  Heisenbergs) the result is the same
• A precise location for an electron cannot be
  determined however regions which describe the
  probable location for electrons can be and these
  regions are known as orbitals.

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Particle in a Box

• We are looking to find a way to describe an
• electrons position.
• This of a 1D box.
• V0 in the box and V8 outside the box.
• This defines the particles a trapped in the box
  and
• it would take an infinite amount of energy to
• remove the particle from the box.

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Particle in a Box
x0
xl
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Schrodingers Method

• Based on the wave properties of the atom
• ? wave function
• H mathematical operator
• E total energy of the atom
• A specific wave function is often called an
  orbital.

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Schrodinger Solutions orbitals

• The Schrodinger equation has many possible
  solutions for a particular atom.
• A solution to the Schrodinger equation is a
  function which satisfies it.
• These wave functions represent orbitals and this
  explains why atoms have several orbitals.
• The functions squared represent the probability
  density of the electrons. We then limit the area
  we describe at the orbital to 90 of the
  probability area.
• These probability functions are used to picture
  in 3D space the probable location of an electron
  and are what is most commonly referred to as an
  orbital.