An increase in the density is seen when moving from Ti to Cu in trans…

The correct answer is Option (3) → Ineffective shielding of d electrons

From Ti to Cu, each next element has one more proton and one more electron, and the electron goes into the inner 3d subshell. A d electron shields the outer electrons from the nucleus poorly, so the effective nuclear charge increases and the atoms are pulled in: the metallic radius decreases slowly along the series.

At the same time the atomic mass increases. A heavier atom packed into a smaller volume means a larger mass per unit volume:

    \( \displaystyle \text{density} = \frac{\text{mass}}{\text{volume}} \)

So the density rises markedly from titanium to copper, and the cause of the shrinking size is the ineffective shielding of the d electrons.

Why the other options are incorrect

• Option (1) lanthanoid contraction — Incorrect. The lanthanoid contraction comes from the filling of 4f orbitals and affects the elements after lanthanum (the third transition series), not the first series Ti to Cu.

• Option (2) filling of f orbitals prior to d orbitals — Incorrect. No f orbitals are filled in the first transition series; 4f filling before 5d belongs to the third series.

• Option (4) Increase in atomic number and atomic size — Incorrect. The atomic number does increase, but the atomic size decreases; a larger size would lower the density, not raise it.

NCERT (2026-27 edition):
Variation in Atomic and Ionic Sizes of Transition Metals – “In general, ions of the same charge in a given series show progressive decrease in radius with increasing atomic number. This is because the new electron enters a d orbital each time the nuclear charge increases by unity. It may be recalled that the shielding effect of a d electron is not that effective, hence the net electrostatic attraction between the nuclear charge and the outermost electron increases and the ionic radius decreases. The same trend is observed in the atomic radii of a given series. … The decrease in metallic radius coupled with increase in atomic mass results in a general increase in the density of these elements. Thus, from titanium (Z = 22) to copper (Z = 29) the significant increase in the density may be noted.”