Write the given electronic configurations

For copper:

$\mathrm{Cu} : [\mathrm{Ar}]\,3d^{10}4s^1$

Therefore,

• $\mathrm{Cu}^+ : [\mathrm{Ar}]\,3d^{10}$
• $\mathrm{Cu}^{2+} : [\mathrm{Ar}]\,3d^9$

Initial expectation from electronic configuration

A completely filled subshell, such as $3d^{10}$, is generally more stable than a partially filled subshell like $3d^9$.

So, based only on electronic configuration, one may think that $\mathrm{Cu}(I)$ should be more stable than $\mathrm{Cu}(II)$.

Actual stability of oxidation states in copper

In transition metal chemistry, the stability of an oxidation state is not decided only by isolated-ion electronic configuration. It also depends strongly on factors such as:

• lattice enthalpy,
• hydration enthalpy,
• bond energies with ligands/anions,
• whether the medium is aqueous or not.

Copper shows both $+1$ and $+2$ states depending on the compound

• In aqueous solution, $\mathrm{Cu}^{2+}$ is generally more stable than $\mathrm{Cu}^+$.
• But in many compounds containing soft ligands/anions, $\mathrm{Cu}^+$ is quite stable, for example:
  • $\mathrm{CuCl}$,
  • $\mathrm{CuBr}$,
  • $\mathrm{CuI}$.

Also, in aqueous medium, $\mathrm{Cu}^+$ tends to disproportionate:

$2\mathrm{Cu}^+ \rightarrow \mathrm{Cu}^{2+} + \mathrm{Cu}$

This shows that relative stability changes with environment.

Evaluate the options

A: $\mathrm{Cu}(II)$ is more stable
This is not universally true for all copper salts.

B: $\mathrm{Cu}(II)$ is less stable
Also not universally true.

C: $\mathrm{Cu}(I)$ and $\mathrm{Cu}(II)$ are equally stable
Incorrect.

D: Stability of $\mathrm{Cu}(I)$ and $\mathrm{Cu}(II)$ depends on nature of copper salts
This is correct, because the relative stability depends on the medium and ligands/anions present.

Final answer

$\boxed{\text{D}}$