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Homework Help: Finding Planck time in terms of [G], [h], and [c]

  1. Jan 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Find a set of 3 exponents a, b, g such that the quantity [G]^a [h]^b [c]^g has dimensions of time. In other words:
    [T] = [G]^a [h]^b [c]^g
    (hint: you should get 3 algebraic equations in the 3 unknowns a, b, g which are not that hard to solve. Now determine the socalled
    Planck time from tPlanck = G^a h^b c^g. [3 Points].

    2. Relevant equations

    G = 6.67266 x 10^-11 m^3 kg^-1 s^-2
    h = 6.62606896x10^-34 kg m^2 s^-1
    c = 299,792,458 m s^-1

    3. The attempt at a solution

    I solved a = 1/2, b = 1/2, g = -5/2, which cancel out the dimensions other than [T],
    and then I tried to calculate the value for Placnk time:

    (6.67266 x 10^-11)^(1/2) (6.62606896x10^-34)^(1/2) (299,792,458)^(-5/2)
    = 1.3512189 x10^-43

    Which is not what it should be.. where did I make a mistake..?
  2. jcsd
  3. Jan 21, 2010 #2


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    You used [itex]h[/itex] rather than [itex]\hbar[/itex].
  4. Jan 24, 2010 #3
    How did you find out those exact values of the exponents?
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