1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook