Concept:
The IUPAC systematic nomenclature for newly discovered elements uses numerical roots corresponding to the digits of the atomic number.
\[
\begin{aligned}
0 \quad &\rightarrow\quad \text{nil} \\
1 \quad &\rightarrow\quad \text{un} \\
2 \quad &\rightarrow\quad \text{bi} \\
3 \quad &\rightarrow\quad \text{tri} \\
4 \quad &\rightarrow\quad \text{quad} \\
5 \quad &\rightarrow\quad \text{pent} \\
6 \quad &\rightarrow\quad \text{hex} \\
7 \quad &\rightarrow\quad \text{sept} \\
8 \quad &\rightarrow\quad \text{oct} \\
9 \quad &\rightarrow\quad \text{enn}
\end{aligned}
\]
The suffix ium is added at the end of the name.
Step 1: Decode the systematic name.
The name
Ununnilium can be divided as:
\[\begin{aligned}
\text{Un} \;-\; \text{Un} \;-\; \text{Nil} \;-\; \text{ium}
\end{aligned}\]
Using the IUPAC roots:
\[\begin{aligned}
\text{Un} &= 1 \\
\text{Un} &= 1 \\
\text{Nil} &= 0
\end{aligned}\]
Step 2: Determine the atomic number.
Combining the digits,
\[\begin{aligned}
110
\end{aligned}\]
Therefore, the atomic number of Ununnilium is
\[\begin{aligned}
\boxed{110}
\end{aligned}\]
Hence, option \(\mathbf{(C)}\) is correct.