To determine the ratio between the number of neutrons present in Carbon-14 ([tex]\(C-14\)[/tex]) and Silicon-28 ([tex]\(Si-28\)[/tex]) atoms, let's go through each step in detail:
1. Identify the number of protons and neutrons in Carbon-14 ([tex]\(C-14\)[/tex]):
- Carbon ([tex]\(C\)[/tex]) has an atomic number of 6, which means it has 6 protons.
- The mass number of Carbon-14 ([tex]\(C-14\)[/tex]) is 14. The mass number represents the total number of protons and neutrons in the nucleus.
- To find the number of neutrons, we subtract the number of protons from the mass number:
[tex]\[
\text{Number of neutrons in } C-14 = 14 - 6 = 8
\][/tex]
2. Identify the number of protons and neutrons in Silicon-28 ([tex]\(Si-28\)[/tex]):
- Silicon ([tex]\(Si\)[/tex]) has an atomic number of 14, which means it has 14 protons.
- The mass number of Silicon-28 ([tex]\(Si-28\)[/tex]) is 28. Similar to the case with Carbon, the mass number represents the total number of protons and neutrons.
- To find the number of neutrons, we subtract the number of protons from the mass number:
[tex]\[
\text{Number of neutrons in } Si-28 = 28 - 14 = 14
\][/tex]
3. Calculate the ratio of the number of neutrons in Carbon-14 to Silicon-28:
- We found that Carbon-14 has 8 neutrons.
- We found that Silicon-28 has 14 neutrons.
- The ratio of neutrons in Carbon-14 to Silicon-28 is thus:
[tex]\[
\text{Ratio} = \frac{\text{Number of neutrons in } C-14}{\text{Number of neutrons in } Si-28} = \frac{8}{14} = \frac{4}{7}
\][/tex]
4. Express the ratio in the simplest form:
- The simplified ratio is [tex]\(4:7\)[/tex].
So, the ratio between the number of neutrons in Carbon-14 and Silicon-28 is [tex]\( \boxed{4:7} \)[/tex].
Therefore, the correct answer is:
B) [tex]\(4:7\)[/tex]
