1. Identify the complexes and oxidation state of chromium

Given:

• $(A) = [Cr(H_2O)_6]Cl_3 \Rightarrow [Cr(H_2O)_6]^{3+}$
• $(B) = [Cr(NH_3)_6]Cl_3 \Rightarrow [Cr(NH_3)_6]^{3+}$

In both, chromium is in oxidation state $+3$.

So, electronic configuration of $Cr^{3+}$ is: $Cr: [Ar]3d^5 4s^1$ $Cr^{3+}: [Ar]3d^3$

2. Magnetic property

For an octahedral $d^3$ configuration: $t_{2g}^3 e_g^0$ Thus, there are three unpaired electrons in both complexes.

So statement B is correct.

3. Compare crystal field splitting $\Delta_0$

From spectrochemical series: $NH_3 > H_2O$ Thus, $NH_3$ is a stronger field ligand than $H_2O$, so: $\Delta_0(B) > \Delta_0(A)$ Hence statement D is correct.

4. Relation between observed color and absorbed color

A complex appears in the color complementary to the color it absorbs.

• $(A)$ appears violet, so it absorbs complementary color (yellow-green region), not violet.
• $(B)$ appears yellow, so it absorbs complementary color (violet region), not yellow.

Therefore statement C is correct.

5. Check statement A

Statement A says:

$\Delta_0$ values of (A) and (B) are calculated from the energies of violet and yellow light, respectively.

This is incorrect because the splitting energy corresponds to the absorbed light, not the observed color.

• For violet-colored complex $(A)$, $\Delta_0$ should be calculated from the energy of its absorbed complementary color, not violet light.
• For yellow-colored complex $(B)$, $\Delta_0$ should be calculated from the energy of its absorbed complementary color, not yellow light.

Hence statement A is incorrect.

6. Final answer

The incorrect statement is: $\boxed{A}$