6.3 The de Broglie Relation, the Heisenberg Uncertainty Principle, and Orbitals

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The de Broglie Equation

The de Broglie equation shows the dependence of the wavelength of a particle of matter on its mass and velocity.

de Broglie equation

The de Broglie equation shows that this wavelength is inversely proportional to both the mass and velocity of the particle (h is Planck's constant, 6.626x10-34J.s).  This explains why this wavelength is so small as to not be observable for large objects.  But for a particle as small as an electron (m = 9.11x10-31kg) the wavelength can be observed and lines up with that predicted by the de Broglie equation.

To obtain a wavelength in meters, be sure to use the mass in kg and the velocity in m/s (all SI units).

The Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle quantifies the limits to which a particle's (usually an electron) position and momentum can simultaneously be known.

Heisenberg Uncertainty Principle

The product of the uncertainties in the position and momentum will be a minimum of h/4ℼ.  This means the greater the precision to which the position is known, the greater the uncertainty in the momentum and vice-versa.  This is by no means intuitive and is just another example that the quantum world is distinctly different than the macro world we experience every day.