To determine the empirical formula, we need to simplify the ratio of the number of atoms of each element in the compound to the smallest whole numbers.
Given the molecular formula \( A_3 B_9 \):
1. Count the number of atoms of each element:
- For element \( A \): there are 3 atoms.
- For element \( B \): there are 9 atoms.
2. Find the greatest common divisor (GCD) of these two numbers (3 and 9). Since 3 is the GCD of both 3 and 9, divide the number of atoms of each element by 3:
- \( \frac{3}{3} = 1 \)
- \( \frac{9}{3} = 3 \)
3. Write the simplified ratio of \( A \) to \( B \) using the results from the division:
- The number of atoms of \( A \) is 1.
- The number of atoms of \( B \) is 3.
Therefore, the empirical formula is \( AB_3 \).
So, the correct answer is:
[tex]\[ AB_3 \][/tex]
