To determine which compound shows color due to d-d transition, we must understand the mechanism behind such color formation. The d-d transition occurs in complexes of transition metals, where electrons jump from one d-orbital to another. This transition requires partially filled d-orbitals and occurs in compounds with transition metals.
Now, let's analyze each given compound:
Thus, the only compound in the given options showing color due to d-d transition is \(\text{CuSO}_4.5\text{H}_2\text{O}\).
Explanation: CuSO$_4$ $\cdot$ 5H$_2$O (copper(II) sulfate pentahydrate) contains the Cu$^{2+}$ ion, which has a partially filled $d$-orbital. The electronic configuration of Cu$^{2+}$ is [Ar] $3d^9$. In an aqueous environment, the Cu$^{2+}$ ion forms a complex with water molecules, creating a distorted octahedral geometry. The $d$-orbitals of the Cu$^{2+}$ ion split into two energy levels due to the ligand field created by the surrounding water molecules. The absorption of visible light causes electrons to transition between these $d$-orbital energy levels ($d$-$d$ transitions), resulting in the characteristic blue colour of the compound.
Other Options: K$_2$Cr$_2$O$_7$ (potassium dichromate), K$_2$CrO$_4$ (potassium chromate), and KMnO$_4$ (potassium permanganate) show colour due to charge transfer transitions, not $d$-$d$ transitions. In these compounds, the chromate and permanganate ions are highly coloured due to the transfer of electrons between the metal and oxygen atoms.
Conclusion: The compound CuSO$_4$ $\cdot$ 5H$_2$O shows colour due to $d$-$d$ transitions.
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)

Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,