To determine the number of oxygen atoms in the chemical formula [tex]\(2 \text{Ca} \left( \text{ClO}_2 \right)_2\)[/tex], let's break down the formula step by step.
1. Identify the components of the formula:
- The chemical formula [tex]\(2 \text{Ca} \left( \text{ClO}_2 \right)_2\)[/tex] consists of calcium (Ca), chlorine (Cl), and oxygen (O).
2. Understand the subscript outside the parentheses:
- The subscript "2" outside the parentheses indicates that everything inside the parentheses [tex]\(( \text{ClO}_2 )\)[/tex] is multiplied by 2.
- Inside the parentheses, there is one chlorine (Cl) atom and two oxygen (O) atoms, which gives us the group [tex]\(( \text{ClO}_2 )\)[/tex].
3. Count the atoms inside a single group [tex]\(( \text{ClO}_2 )_2\)[/tex]:
- For one group of [tex]\(( \text{ClO}_2 )_2\)[/tex], we have:
[tex]\[
2 \times (\text{ClO}_2) = 2 \text{Cl} + 2 \times 2 \text{O}
\][/tex]
- This results in:
[tex]\[
2 \text{Cl} + 4 \text{O}
\][/tex]
4. Multiply by the number of such groups:
- Since there are 2 groups of [tex]\(( \text{ClO}_2 )_2\)[/tex] in the original formula:
[tex]\[
2 \times \left( 2 \text{Cl} + 4 \text{O} \right)
\][/tex]
- This results in:
[tex]\[
(2 \times 2) \text{Cl} + (2 \times 4) \text{O}
\][/tex]
- Breaking that down gives us:
[tex]\[
4 \text{Cl} + 8 \text{O}
\][/tex]
Thus, the total number of oxygen atoms in the chemical formula [tex]\(2 \text{Ca} \left( \text{ClO}_2 \right)_2\)[/tex] is [tex]\(8\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{8}
\][/tex]
