1. Recall the modern Periodic Law

   The modern periodic law states:

   $\text{The physical and chemical properties of elements are periodic functions of their atomic numbers.}$

2. Interpret the statement

   This means that when elements are arranged in order of increasing atomic number $Z$, their properties repeat periodically.

3. Check the options

   • A: nuclear masses — Incorrect. Periodic properties are not based on nuclear mass.
   • B: atomic numbers — Correct. Modern periodic law is based on atomic number.
   • C: nuclear neutron-proton number ratios — Incorrect. This is not the basis of periodicity.
   • D: atomic masses — Incorrect for the modern periodic law. This was the basis of Mendeleev’s earlier periodic classification, but not the modern law.

4. Final conclusion

   Therefore, according to the Periodic Law of elements, variation in properties is related to their:

   $\boxed{\text{atomic numbers}}$

So, the correct option is B.