Planck's constant

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15:47 — by Dennis H.

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Key Questions

  • Answer:

    Planck's constant is #h~~6.63*10^-34 \ "J"*"s"#.

    Explanation:

    Planck's constant, in science, is denoted by #h#, and is given the value of

    #h~~6.63*10^-34 \ "J"*"s"#

    Note that #1 \ "J"=1 \ "N"*"m"#

    #=1 \ "kg"*"m/s"^2*"m"#

    #=1 \ "kg"*"m"^2"/s"^2#

    And so, we can rewrite #h# as

    #h~~6.63*10^-34 \ "kg"*"m"^2"/s"^2*"s"#

    #=6.63*10^-34 \ "kg"*"m"^2*"s"^-1#

    This is one of the smallest constants in physics, and gives the relationship between a photon's energy and its frequency.

    Source: https://en.wikipedia.org/wiki/Planck_constant

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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.

Questions

  • MetaPhysik answered · 3 months ago