The Planck mass is the natural unit of mass, denoted by m_P. It is the mass for which the Schwarzschild radius is equal to the Compton length divided by π;.

$m\_P\; =\; \backslash sqrt\{\backslash frac\{\backslash hbar\; c\}\{G\}\}$ ≈ 1.2209 × 10¹⁹ GeV/c² = 2.176 × 10^-8 kg

The 2002 CODATA-recommended value for the Planck mass is 2.176 45(16) × 10^-8 kg, where the part in parentheses indicates the uncertainty in the last digits shown — that is, a value of 2.17645 × 10^-8 kg ± 0.00016 × 10^-8 kg.

Particle physicists and cosmologists often use the reduced Planck mass, which is

$\backslash sqrt\{\backslash frac\{\backslash hbar\{\}c\}\{8\backslash pi\; G\}\}$ ≈ 4.340 µg.

Adding the 8π simplifies several equations in gravity.

Unlike most of the other Planck units, the Planck mass is on a scale more or less conceivable to humans, as the body mass of a flea is roughly 4000 to 5000 m_P.

Significance

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The Planck mass is the mass of a black hole whose Schwarzschild radius multiplied by π equals its Compton wavelength. The radius of such a black hole is roughly the Planck length, which is believed to be the length scale at which both general relativity and quantum mechanics simultaneously become important.

See also

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• Planck unit
• Planck length
• Planck particle
• Orders of magnitude (mass)

External links

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• The NIST Reference on Constants, Units, and Uncertainty

Physical constants | Natural units | Units of mass

Massa de Planck | Masse de Planck | 플랑크 질량 | Massa planckiana | プランク質量 | Planck-tömeg | Masa Plancka | Planck mass | Khối lượng Planck | 蒲朗克質量