Planck Mass

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

mP = 2.18 × 108 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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