Question

What units can be derived from the constants c, G and h?

Answer 1

Combinations of c, G and h can yield the squares of mass, time and distance.

Explanation:

Let's look at the three constants in terms of SI units.

The speed of light `c` has units: `m/s`

The gravitational constant `G` has units: `m^3/(kgs^2)`

Planck's constant `h` has units: `(m^2kg)/s`

Let's combines these in different ways:

The square of the unit of length is given by:
`(Gh)/c^3` which has units `m^3/(kgs^2)(m^2kg)/ss^3/m^3=m^2`

The square of the unit of time is given by:
`(Gh)/c^5` which has units `m^3/(kgs^2)(m^2kg)/ss^5/m^5=s^2`

The square of the unit of mass is given by:
`(hc)/G` which has units `(m^2kg)/sm/s(kgs^2)/m^3=kg^2`