# Planck energy

In physics, Planck energy, denoted by EP, is the unit of energy in the system of natural units known as Planck units.[1]

EP is a derived, as opposed to basic, Planck unit. It is defined by:

${\displaystyle E_{\mathrm {P} }={\sqrt {\frac {\hbar c^{5}}{G}}},}$

where c is the speed of light in a vacuum, ћ is the reduced Planck's constant, and G is the gravitational constant.

Substituting values for the various components in this definition gives the approximate equivalent value of this unit in terms of other units of energy:

${\displaystyle 1\ E_{\mathrm {P} }\approx 1.956\times 10^{9}\ \mathrm {J} \approx 1.2209\times 10^{19}\ \mathrm {GeV} \approx 543.36\ \mathrm {kWh} }$[2]

An equivalent definition is:

${\displaystyle E_{\mathrm {P} }={\frac {\hbar }{t_{\mathrm {P} }}},}$

where tP is the Planck time.

Also:

${\displaystyle E_{\mathrm {P} }={m_{\mathrm {P} }}{c^{2}},}$

where mP is the Planck mass.

The ultra-high-energy cosmic ray observed in 1991 had a measured energy of about 50 joules, equivalent to about 2.5×10−8 EP.[3] Most Planck units are extremely small or extremely large, as in the case of Planck temperature and Planck acceleration. Theoretically, the highest energy photon carries one unit of Planck energy (see Ultra-high-energy gamma ray). For comparison the energy of 1 EP is approximately equal to the energy stored in an automobile gas tank (57.2 L of gasoline at 34.2 MJ/L of chemical energy).

Planck units are designed to normalize the physical constants G, ћ and c to 1. Hence given Planck units, the mass-energy equivalence E = mc² simplifies to E = m, so that the Planck energy and mass are numerically identical. In the equations of general relativity, G is often multiplied by 4π. Hence writings in particle physics and physical cosmology often normalize G to 1. This normalization results in the reduced Planck energy, defined as:

${\displaystyle {\sqrt {\frac {\hbar {}c^{5}}{4\pi G}}}\approx 7.80\times 10^{8}\ \mathrm {J} \approx 4.86\times 10^{18}\ \mathrm {GeV} \approx 216.28\ \mathrm {kWh} .}$

## References

1. ^ "Planck Energy". Cosmos, The SAO Encyclopedia, Swinburne University of Technology. Retrieved 18 September 2015.
2. ^ "CODATA Value: Planck mass energy equivalent in GeV". physics.nist.gov. Retrieved 2016-12-21.
3. ^ "HiRes - The High Resolution Fly's Eye Ultra High Energy Cosmic Ray Observatory". www.cosmic-ray.org. Retrieved 2016-12-21.