Question

Dimensional Analysis: Call m_{Planck} the unit of mass
in a system of units in which G, c and h, all have the value 1
times the combination of units with the appropriate dimensions.
What is the volume in SI units of a mass of water equal to
m_{Planck}? What is the volume in SI units of
m_{Planck} of air? (Answer should be in SI unit)

Answer #1

**Plancks units of Mass are defined in fundamental
constants in Planck units** as

( where )

Then in SI units, m_{p} has the value as

a). Now when mass of water= mPlanck= m_{p}

or

Density of water is

Then we know that Volume= Mass/ Density

Using all known values, Volume of water is
**(ANS)**

b).Now when mass of air= mPlanck= m_{p}

or

Density of air is

Then we know that Volume= Mass/ Density

Using all known values, Volume of air is
**(ANS)**

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Answer is not 0.323 mL I tried this and it didnt work!!

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