Planck Mass

on . Posted in Quantum Mechanics

Planck mass, abbreviated as \(m_p\), is a fundamental unit of mass in the system of natural units known as Planck units. It derived from fundamental physical constants such as the speed of light, the gravitational constant, and the reduced Planck constant.

The Planck mass is significant because it represents the mass of a hypothetical particle whose Compton wavelength (the wavelength associated with its quantum mechanical nature) is equal to its Schwarzschild radius (the radius at which its gravitational pull becomes strong enough to form a black hole).  At the Planck scale, where the Planck mass is relevant, quantum gravitational effects are expected to dominate, and conventional notions of mass and gravity might no longer apply in the same way as in classical physics.  Therefore, the Planck mass plays a role in theories of quantum gravity and the fundamental structure of spacetime.


Planck Mass Formula

\( m_p = \sqrt{  h\;c \;/\; G  } \)     (Plank Mass)

\( h =   m_p^2 \;  ( G \;/\; c )  \)

\( c =   m_p^2 \; G \;/\; h  \)

\( G =  h\;c \;/\; m_p^2  \)

Symbol English Metric
\( m_p \) = Planck mass (See Physics Constants) \(lbm\) \(kg\)
\( h \) = Planck constant \(lbf-ft\;/\;sec\) \(J-s\)
 \( c \) = speed of light in vacuum \(ft\;/\;sec\)  \(m\;/\;s\)
\( G \) = gravitational constant \(lbf-ft^2\;/\;lbm^2\) \(N - m^2\;/\;kg^2\)


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