Planck's constant

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Planck's Equation

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Key Questions

  • Planck's constant is used to relate the energy of light to its frequency, using the equation

    E = h𝛎

    Where E is the energy of a photon in Joules, h is Planck's constant (6.626 x #10^(-34)# J s) and 𝛎 is the frequency of light in Hertz (or /sec).

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  • Answer:

    Planck's constant is instrumental and an unavoidable constant which appears in quantum mechanics.

    Explanation:

    Even though it was first introduced in the Planck's law,

    #u_(lamda)d(lamda) = (8pihc)/lamda^5*(dlamda)/(e^((hc)/(lamdakT))-1)#

    Where one quantum of radiation would have an energy, #E = (hc)/(lamda)#, the concept of quantized radiation was extended by Einstein, later by Bohr in their theories as a part of the old quantum theory.

    Today almost all important relationships in quantum mechanics, contain Planck's constant (or the reduced Planck's constant #h/(2pi)#).

    Examples would include,

    1) de Broglie relation -
    #lamda = h/p#

    2) Schrodinger equation -

    #(ih)/(2pi)(delpsi)/(delt) = -(h^2)/(8pi^2m)(nabla)^2psi + V(vec r,t)psi#

    3) Commutator of #x# and #p_x# -

    #[x,p_x] = (ih)/(2pi)#

    And so on.

    It is to quantum mechanics, what the constants #epsilon_0# and #mu_0# are to Electricity and Magnetism.

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