To solve the problem, follow these steps:
1. Understand the ratio:
The ratio of protons to neutrons in one atom of Element Z is given as 3:4. This means for every 3 protons, there are 4 neutrons.
2. Given information:
We are informed that a cluster of atoms of Element Z contains 12 protons.
3. Set up the relationship using the ratio:
- The given ratio of protons to neutrons indicates that if there are 3 protons, there should be 4 neutrons.
- We need to determine how many sets of 3 protons are present in the cluster with 12 protons.
4. Calculate the ratio factor:
- Determine how many times the ratio of 3 protons fits into 12 protons.
- This can be calculated by dividing the number of protons in the cluster by the number of protons in the ratio: [tex]\( \frac{12}{3} = 4 \)[/tex].
- This value (4) represents how many groups of 3 protons we have in the cluster.
5. Use the ratio factor to find the number of neutrons:
- Since each group of 3 protons is associated with 4 neutrons, we multiply the ratio factor (4) by the number of neutrons in the ratio: [tex]\( 4 \times 4 = 16 \)[/tex].
Therefore, the number of neutrons in the cluster containing 12 protons is 16.
The correct answer is D) 16.
