Making sense of the unfamiliar
The quantity (hG/c5)1/2 is of some physical significance. What can you say about it?
[The symbols h, G and c have their usual significance.]
Solution
Reveal

Solution
Even though you’re unlikely to have met this combination of fundamental constants before, there are two useful things you can say about it: you can figure out its units; and you can work out its magnitude.
Consider its units first of all.
The units of h are:
The units of G are:
The units of c are:
Thus the units of (hG/c5)1/2 are
![\[ \left(\frac{\left[ m^2\cdot kg \cdot s^{-1}\right] \cdot\left[m^3\cdot kg^{-1} \cdot s^{-2}\right]}{\left[m \cdot s^{-1} \right]^5}\right)^{1/2} = s \]](mastermathpng-0.png)
So this quantity is a time. Let’s call it τp for short.
Substituting in the values of the fundamental constants we find-
![\[ \tau _p = \left( \frac{ 6.63 \times 10 ^{-34} \times 6.67 \times 10 ^{-11}}{\left [ 3 \times 10 ^8\right]^5}\right)^{1/2} = 1.35 \times 10^{-43} s \]](mastermathpng-1.png)
So it is a very short time!
To within a factor of 2π, τp is what is known as the Planck time; it represents the age of the universe at which, thinking backwards towards its big-bang-birth, our current formulation of physics ceases to apply.