(adsbygoogle = window.adsbygoogle || []).push({}); 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..?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**