Number of quantum states

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Homework Statement



In lecture for stats and thermal, we briefly talked about quantum states and went through an example. However, the lecturer simply told us the answer to the second part of the question without going through it. Here's the question:

1a.) How many molecules of H2O are in 500cm^3 of water?

1b.) How many quantum states are there between zero and energy of this water?

Homework Equations



density = m/V

The Attempt at a Solution



Using density as 1000kgm^-3, I worked out the answer to be 1.67x10^26 molecules, which he said was correct.

He said that the answer to the second part is 4.56x10^28 , but I couldn't see why.

THanks.
 

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