To determine the coordination environment of the \( \text{Ca}^{2+} \) ion in its complex with \( \text{EDTA}^{4-} \), we need to understand how \( \text{EDTA}^{4-} \) acts as a ligand and coordinates with metal ions.
Step 1: Understanding EDTA as a ligand.
Step 2: Coordination Geometry of \( \text{Ca}^{2+} \) with EDTA.
Step 3: Conclusion and Verification.
Thus, the correct answer is that the coordination environment of \( \text{Ca}^{2+} \) ion in its complex with \( \text{EDTA}^{4-} \) is octahedral.
To determine the coordination environment of the \( \text{Ca}^{2+} \) ion in its complex with \( \text{EDTA}^{4-} \), we need to understand the structure and binding nature of \( \text{EDTA}^{4-} \).
\( \text{EDTA}^{4-} \) (ethylenediaminetetraacetic acid) is a hexadentate ligand, which means it can form six bonds with a metal ion. It does this by using its four carboxylate groups and two amine groups. This ability to form six coordinate bonds with a metal ion typically leads to an octahedral geometry.
Let's evaluate each option:
Based on the above analysis, the correct choice is \(octahedral\) because \( \text{EDTA}^{4-} \) provides six coordination sites equating to an octahedral coordination environment.
The given circuit works as: 
Let the lines $L_1 : \vec r = \hat i + 2\hat j + 3\hat k + \lambda(2\hat i + 3\hat j + 4\hat k)$, $\lambda \in \mathbb{R}$ and $L_2 : \vec r = (4\hat i + \hat j) + \mu(5\hat i + + 2\hat j + \hat k)$, $\mu \in \mathbb{R}$ intersect at the point $R$. Let $P$ and $Q$ be the points lying on lines $L_1$ and $L_2$, respectively, such that $|PR|=\sqrt{29}$ and $|PQ|=\sqrt{\frac{47}{3}}$. If the point $P$ lies in the first octant, then $27(QR)^2$ is equal to}