220px-Max Planck 1933

Max Planck

The Planck units are a system of units based on five fundamental constants, named after their inventor Max Planck:

  • The speed of light in a vacuum c, which is equal to exactly 299792458 meters per second
  • The gravitational constant G, approximately equal to \(6.67408 \times 10^{-11}\) meters cubed per kilogram per second squared
  • The reduced Planck constant ħ, approximately equal to \(1.05457 \times 10^{-34}\) joule-seconds
  • The Coulomb constant ke, approximately equal to \(8.98755 \times 10^9\) meters per farad
  • The Boltzmann constant kB, approximately equal to \(1.380649 \times 10^{-23}\) joules per kelvin

Below you can see some Planck units:

  • Planck length \(l_{P} =\sqrt\frac{\hbar G}{c^3} \approx 1.616 \times 10^{-35}\) m,
  • Planck time \(t_{P} = \sqrt{\frac{\hbar G}{c^5}}\approx 5.391 \times 10^{-44}\) s,
  • Planck mass \(m_{P}=\sqrt{\frac{\hbar c}{G}}\approx 2.176470 \times 10^{-8}\) kg,
  • Planck energy \(E_{P} = m_{P} c^2 = \frac{\hbar}{t_{P}} = \sqrt{\frac{\hbar c^5}{G}}\approx 10^{19}\)GeV,
  • Planck temperature \(T_{P} = \frac{m_{P} c^2}{k_B} = \sqrt{\frac{\hbar c^5}{G k_B^2}}\approx 1.416808 \times 10^{32}\) K.

By relating these units using dimensional analysis, a system of units can be created. Some Planck units are very small (example: the Planck volume, equal to about \(4.222 \times 10^{-105}\) cubic meters), but some are very large (example: the Planck pressure, equal to about \(4.633 \times 10^{113}\) pascals).[1]

Sources Edit

Large numbers in science

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