Planck Mass

The Planck mass is the fundamental unit of mass in the system of Planck units. It has the value:

mP = 2.18 × 10-8 kg

In SI units, measurements of mass are made in kilograms (usually given the symbol kg). While the kilogram is convenient for use in everyday life, such as measuring the mass of a person or the mass of ingredients for a cake, it becomes less practical when we discuss the masses of the elementary particles such as the proton (rest mass of 1.67 × 10-27 kg) and the electron (rest mass about 1/1800 that of the proton).

A consequence of using kilograms to measure mass is that the fundamental constants take on values that are not always convenient for including in equations:

Speed of light c = 299792458 ms-1
Gravitational constant G = 6.673(10) x 10-11 m3 kg-1 s-2
Plank’s constant (reduced) $ \hbar $ = h/2π = 1.054571596(82) x 10-34 kg m2 s-1
Boltzmann constant k = 1.3806502(24) x 10-23 kg m2 s-2 K-1

The Planck mass is derived dimensionally using combinations of these fundamental constants:

$ m_p_= \sqrt{\frac{\hbar c}{G}} $

By redefining the base units for length, mass and time in terms of the Planck units, the fundamental constants have the values: c = G = $ \hbar $ = k = 1.

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