Sure! Let's calculate the neutron-to-proton ratio for each given atom step by step. The neutron-to-proton ratio is determined by the formula:
[tex]\[ \text{Neutron-to-Proton Ratio} = \frac{\text{Number of Neutrons}}{\text{Number of Protons}} \][/tex]
We need two pieces of information for each atom: the mass number and the number of protons. The number of neutrons can be found by subtracting the number of protons from the mass number:
[tex]\[ \text{Number of Neutrons} = \text{Mass Number} - \text{Number of Protons} \][/tex]
Let's go through each atom one by one.
### a. Tin-134
- Mass Number: 134
- Number of Protons: 50
Calculate the number of neutrons:
[tex]\[ \text{Number of Neutrons} = 134 - 50 = 84 \][/tex]
Now, calculate the neutron-to-proton ratio:
[tex]\[ \text{Neutron-to-Proton Ratio} = \frac{84}{50} = 1.68 \][/tex]
### b. Silver-107
- Mass Number: 107
- Number of Protons: 47
Calculate the number of neutrons:
[tex]\[ \text{Number of Neutrons} = 107 - 47 = 60 \][/tex]
Now, calculate the neutron-to-proton ratio:
[tex]\[ \text{Neutron-to-Proton Ratio} = \frac{60}{47} \approx 1.2766 \][/tex]
### c. Carbon-12
- Mass Number: 12
- Number of Protons: 6
Calculate the number of neutrons:
[tex]\[ \text{Number of Neutrons} = 12 - 6 = 6 \][/tex]
Now, calculate the neutron-to-proton ratio:
[tex]\[ \text{Neutron-to-Proton Ratio} = \frac{6}{6} = 1.0 \][/tex]
### d. Carbon-14
- Mass Number: 14
- Number of Protons: 6
Calculate the number of neutrons:
[tex]\[ \text{Number of Neutrons} = 14 - 6 = 8 \][/tex]
Now, calculate the neutron-to-proton ratio:
[tex]\[ \text{Neutron-to-Proton Ratio} = \frac{8}{6} \approx 1.3333 \][/tex]
### Summary of Results
- Tin-134: Neutron-to-Proton Ratio ≈ 1.68
- Silver-107: Neutron-to-Proton Ratio ≈ 1.2766
- Carbon-12: Neutron-to-Proton Ratio = 1.0
- Carbon-14: Neutron-to-Proton Ratio ≈ 1.3333
