## Actual Sizes of Molecules and Atoms

Dicembre 18th, 2020 | by Marcello Colozzo |

Exercises in nuclear reactor physics by Ing. Giorgio Bertucelli

Exercise

Find the size of a water molecule if the molecular mass and density of water at melting point are approximately 18 and 1g/cm³

Solution
One gram-mole of water is 18 g_{m}. It occupies a volume of 18/1=18cm³. Since at the melting point the molecules are closely packed the volume of each molecule, assumed cubical, would be approximately

If each molecule were assumed spherical (more nearhly true) its volume would be roughly 2/3 of the above; so the radius of the molecule is

Exercise

Calculate the mass of CZ=6A=12 nucleus in grams.

Solution
mass of the electron=0.00054876 amu
mass of CZ=6A=12 atom=14.007682 amu
mass of CZ=6A=12 nucleus =14.007682-60.00054876=14.004394 amu
=14.004394 amu ·1,6598310?²4g /amu=2.32449·10?²³g

Example
From a partial list of isotopes we can read

The chemical atomic masses (4th column) are based on 16,000 for Oxygen as it occurs in nature, i.e. as a mixture of the isotopes O16,O17,O18. This is called the chemical scale. On the other hand, the isotope masses (6th column) show the mass of O16 to be 16.000. This is called the physical scale.
Let us calculate the weighted mass of naturally occurring Oxygen by using physical scale and the abundance percentage (7th column).

Notation

In nuclears calculations the physical scale is used.

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