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Download QR code; Print/export ... Photon momentum p = momentum of photon (kg m s −1) ... Equation Angular momentum quantum numbers:
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
The classical formulae for the energy and momentum of electromagnetic radiation can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change ...
This equation is known as the Planck relation. Additionally, using equation f = c/λ, = where E is the photon's energy; λ is the photon's wavelength; c is the speed of light in vacuum; h is the Planck constant; The photon energy at 1 Hz is equal to 6.626 070 15 × 10 −34 J, which is equal to 4.135 667 697 × 10 −15 eV.
The photon having non-zero linear momentum, one could imagine that it has a non-vanishing rest mass m 0, which is its mass at zero speed. However, we will now show that this is not the case: m 0 = 0. Since the photon propagates with the speed of light, special relativity is called for. The relativistic expressions for energy and momentum ...
This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m 0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime [ 1 ] [ 2 ] [ 3 ] and that the particles are free.
Several approaches exist as a means of describing the motion of single and multiple relativistic particles, with a prominent example being postulations through the Dirac equation of single particle motion. [2] Since the energy-momentum relation of an particle can be written as: [3]
Then the uncertainty relation for position and momentum says that , so the uncertainty in the particle's momentum satisfies . Using the relativistic relation between momentum and energy E 2 = ( pc ) 2 + ( mc 2 ) 2 , when Δ p exceeds mc then the uncertainty in energy is greater than mc 2 , which is enough energy to create another particle of ...