Planck particle


A Planck particle, or planckion, named after physicist Max Planck, is a hypothetical particle defined as a tiny black hole whose Compton wavelength is equal to its Schwarzschild radius. Its mass is thus approximately the Planck mass, and its Compton wavelength and Schwarzschild radius are about the Planck length. Planck particles are sometimes used as an exercise to define the Planck mass and Planck length. They play a role in some models of the evolution of the universe during the Planck epoch.
Compared to a proton, for example, the Planck particle would be extremely small and massive. The Planck particle would also have a very fleeting existence, evaporating due to Hawking radiation after approximately.

Derivation

While opinions vary as to its proper definition, the most common definition of a Planck particle is a particle whose Compton wavelength is equal to its Schwarzschild radius. This sets the relationship:
Thus making the mass of such a particle:
This mass will be times as large as the Planck mass, making a Planck particle 1.772 times as massive as the Planck unit mass.
Its radius will be the Compton wavelength:
The Planck length is defined as

Dimensions

Using the above derivations we can substitute the universal constants h, G, and c, and determine physical values for the particle's mass and radius. Assuming this radius represents a sphere of uniform density, we can further determine the particle's volume and density.
ParameterDimensionExpressionValue in SI unitsValue in Planck units
MassM1.7724
RadiusL3.5449
Maximum chargeQ1.7724
VolumeL3186.6137
LifetimeT89524.9652