1. Interpret the statement

   The phrase "reduction in atomic size with increase in atomic number" refers to a situation where, as we move across a series of elements, the atomic radii decrease instead of increasing.

2. Recall the relevant periodic trend

   This behavior is especially characteristic of the lanthanoids due to lanthanoid contraction.

   • In the lanthanoid series, electrons are added to the $4f$ subshell.
   • The $4f$ electrons shield the nuclear charge very poorly.
   • Therefore, with increasing atomic number, the effective nuclear charge felt by outer electrons increases.
   • As a result, the atomic size gradually decreases.

3. Match with the given options

   • A: $d$-block
     Not generally described by this special contraction phenomenon.

   • B: $f$-block
     Correct, because the lanthanoids belong to the $f$-block and show a steady decrease in atomic size with increasing atomic number.

   • C: Radioactive series
     Not a periodic trend classification for atomic size reduction.

   • D: High atomic masses
     High atomic mass is not the reason or the characteristic series showing this trend.

4. Conclusion

   The reduction in atomic size with increase in atomic number is characteristic of $f$-block elements (specifically lanthanoids).

$\boxed{\text{B}}$

5. Comparison with stored correct answer

   • Derived answer: B
   • Stored correct answer: D

   These do not match. The stored answer appears incorrect because the described trend is the well-known lanthanoid contraction, which is a property of the $f$-block elements, not of elements with high atomic masses.