Planck's Constant

  • Planck's constant, h, appears throughout quantum mechanics and is one of the fundamental constants of physics. It has a value of:

    h = 6.6260693(11) x 10-34 J s

    where uncertain values in the decimal place are contained in brackets. Planck's constant has the units of action ( energy x time, which can be shown to be the same as momentum x length ).

    Planck's constant was first identified as part of Max Planck's description of blackbody radiation. Later, it was shown by Albert Einstein to be the constant of proportionality between the energy ( E ) and frequency ( f ) of photons:

    E = hf

    A closely-related quantity (usually pronounced "h-bar") is:

    ħ = h/2π = 1.054571596(82) x 10-34J s

    In this form, Planck's (reduced) constant appears in the two uncertainty relationships:

    ΔxΔp ≥ ħandΔEΔt ≥ ħ

    where we have uncertainties in the measurements of a particle's
    or wave-packet's position Δx, momentum Δp, energy ΔE and lifetime Δt.

    In Planck units, or natural units, ħ = 1, c = 1.


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