The statement that is not correct for the periodic classification of elements is

For transition elements the d-subshells are filled with electrons monotonically with increase in atomic number.

The correct answer is option 3. For transition elements the d-subshells are filled with electrons monotonically with increase in atomic number.

Let us analyze each of the given statements about the periodic classification of elements in detail:

1. The properties of elements are the periodic functions of their outer electronic configurations.

This statement is correct. The periodic table is arranged in such a way that elements with similar outer electronic configurations fall into the same group and exhibit similar chemical properties. The periodicity in properties arises because elements in the same group have similar valence electron configurations.

2. Non-metallic elements are lesser in number than metallic elements.

This statement is correct. The majority of the elements in the periodic table are metals. Non-metals are fewer and are located primarily on the right side of the periodic table, in the p-block. Metalloids form a small bridge between metals and non-metals.

3. For transition elements, the d-subshells are filled with electrons monotonically with an increase in atomic number.

This statement is incorrect. The filling of the d-subshells in transition elements does not always proceed monotonically with the increase in atomic number due to the stability provided by half-filled and fully filled d-subshells, as well as electron-electron interactions.

For example, chromium (Cr, atomic number 24) has an electron configuration of [Ar] 3d⁵ 4s¹ instead of the expected [Ar] 3d⁴ 4s². Similarly, copper (Cu, atomic number 29) has an electron configuration of [Ar] 3d¹⁰ 4s¹ instead of [Ar] 3d⁹ 4s². These exceptions occur because a half-filled (d⁵) and fully filled (d¹⁰) d-subshell provide extra stability to the atom.

4. The first ionization energies of elements along a period do not vary in a regular manner with the increase in atomic number.

This statement is correct. While there is a general trend for ionization energy to increase across a period (from left to right), there are notable exceptions. For example, the first ionization energy of boron is less than that of beryllium, and the first ionization energy of oxygen is less than that of nitrogen. These irregularities are due to the specific electron configurations and the stability associated with half-filled and fully filled orbitals.

To sum up, the incorrect statement is (3) because the electron filling order in transition elements does not follow a simple, monotonically increasing pattern due to various stabilizing effects that come into play.