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Inorganic Chemistry

Lecture 3

Introduction to Quantum Mechanics and Schrodinger Equation

Useful paragraphs

An Introduction to Quantum Mechanics

The wave-nature of electrons
The quantum theory of radiation introduced by Max Planck and Albert Einstein implies a particle theory of light, in addition to the wave theory of light required by the phenomena of interference and diffraction. In 1924, Louis de Broglie argued that if light were composed of particles and yet showed wave-like properties, the same should be true of electrons and other particles. This phenomenon is referred to as wave–particle duality. The de Broglie relationship combines the concepts of classical mechanics with the idea of wave-like properties by showing that a particle with momentum mv (m = mass and v = velocity of the particle) possesses an associated wave of wavelength ?.
? = h /mv
where h is the Planck constant.
An important physical observation which is a consequence of the de Broglie

relationship is that electrons accelerated to a velocity of 6 x106 m s-1 (by a

potential of 100 V) have an associated wavelength of 120 pm and such

electrons are diffracted as they pass through a crystal. This phenomenon is the

basis of electron diffraction techniques used to determine structures of chemical

compounds.


The uncertainty principle
If an electron has wave-like properties, there is an important and difficult consequence: it becomes impossible to know exactly both the momentum and position of the electron at the same instant in time. This is a statement of Heisenberg’s uncertainty principle. In order to get around this problem,
rather than trying to define its exact position and momentum, we use the probability of finding the electron in a given volume of space. The probability of finding an electron at a given point in space is determined from the function ?2 where ? is a mathematical function which describes the behaviour of an electron-wave; ? is the wavefunction.
The Schrodinger wave equation
Information about the wavefunction is obtained from the Schrodinger wave equation, which can be set up and solved either exactly or approximately; the Schrodinger equation can be solved exactly only for a species containing a nucleus and only one electron i.e. a hydrogen-like system.

A hydrogen-like atom or ion contains a nucleus and only one electron.

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