# Feynman Lectures Vol I 41-4: Find the number of collisions received by a water molecule per second

The reader may easily verify that the number of collisions a single molecule of water receives in a second is about $10^{14}$.

This may be discussed in the exercises, but there has been very little in the Lectures, to this point, which would suggest an approach to finding this number. Indeed, I'm not completely sure what the statement means. For example, in the following chapter the "volume occupied" by one molecule of liquid is the inverse of the number of molecules per volume. That suggests that the molecules are always in mutual contact. What, then, is meant by a liquid molecule receiving a collision?

Even if I had some notion of what a collision really meant, I'm not sure how the reader is expected to determine the number per second. I might be able to come up with a way of solving the problem, but I would like to know what approach Feynman intended in this context.

Any suggestions?

• Indeed they assign difficult problems at Caltech. For example, the exercises for the Feynman Lectures ask for a proof of the Kepler conjecture in the first chapter. Not explaining that it had gone unproven for centuries. My approach to estimating the number of collisions was to treat the molecule like an oscillator confined to a box and find the Planck frequency associated with the average energy per molecule. I reasoned that each complete oscillation would constitute two collisions. The result was $3.75\times 10^{13}$. Commented Mar 29, 2018 at 1:23