In the given equation:
\[ 4K + O_2 \rightarrow 2K_2O \]
we can analyze the ratio of potassium (K) atoms to oxygen (O) atoms.
- From the reactants, there are 4 potassium atoms (4K) and 2 oxygen atoms (from O\(_2\), which has 2 oxygen atoms).
- In the products, each molecule of potassium oxide (K\(_2\)O) contains 2 potassium atoms and 1 oxygen atom. Therefore, with 2 K\(_2\)O molecules, there are also 4 potassium atoms (2 K\(_2\)O × 2 K each) and 2 oxygen atoms (2 K\(_2\)O × 1 O each).
Now, we can summarize the counts:
- Total potassium atoms = 4
- Total oxygen atoms = 2
To find the ratio of potassium atoms to oxygen atoms, we calculate:
\[ \text{Ratio of K to O} = \frac{\text{Number of K atoms}}{\text{Number of O atoms}} = \frac{4}{2} = 2 \]
Thus, the ratio of atoms of potassium to atoms of oxygen is:
2:1
So the correct answer is 2:1.