Answer :
To compare the sulfur isotopes [tex]\(\mathrm{{}^{32}S}\)[/tex] and [tex]\(\mathrm{{}^{35}S}\)[/tex], we need to determine the number of protons and neutrons in each isotope.
### Step-by-Step Solution:
1. Identify the atomic number of sulfur:
- Sulfur has an atomic number of 16, which means every sulfur atom has 16 protons.
2. Determine the number of protons in each isotope:
- [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 protons.
- [tex]\(\mathrm{{}^{35}S}\)[/tex] also has 16 protons.
3. Calculate the number of neutrons in each isotope:
- The number of neutrons is the difference between the mass number and the number of protons.
For [tex]\(\mathrm{{}^{32}S}\)[/tex]:
[tex]\[ \text{Neutrons in } \mathrm{{}^{32}S} = 32 \text{ (mass number)} - 16 \text{ (protons)} = 16 \text{ neutrons} \][/tex]
For [tex]\(\mathrm{{}^{35}S}\)[/tex]:
[tex]\[ \text{Neutrons in } \mathrm{{}^{35}S} = 35 \text{ (mass number)} - 16 \text{ (protons)} = 19 \text{ neutrons} \][/tex]
4. Compare the options given:
- Option A: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 32 protons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 35 protons. (Incorrect, both have 16 protons)
- Option B: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 protons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 protons. (Incorrect, both have 16 protons)
- Option C: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 32 neutrons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 35 neutrons. (Incorrect, [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 neutrons and [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 neutrons)
- Option D: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 neutrons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 neutrons. (Correct)
The correct comparison of the sulfur isotopes [tex]\(\mathrm{{}^{32}S}\)[/tex] and [tex]\(\mathrm{{}^{35}S}\)[/tex] is given in Option D: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 neutrons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 neutrons.
### Step-by-Step Solution:
1. Identify the atomic number of sulfur:
- Sulfur has an atomic number of 16, which means every sulfur atom has 16 protons.
2. Determine the number of protons in each isotope:
- [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 protons.
- [tex]\(\mathrm{{}^{35}S}\)[/tex] also has 16 protons.
3. Calculate the number of neutrons in each isotope:
- The number of neutrons is the difference between the mass number and the number of protons.
For [tex]\(\mathrm{{}^{32}S}\)[/tex]:
[tex]\[ \text{Neutrons in } \mathrm{{}^{32}S} = 32 \text{ (mass number)} - 16 \text{ (protons)} = 16 \text{ neutrons} \][/tex]
For [tex]\(\mathrm{{}^{35}S}\)[/tex]:
[tex]\[ \text{Neutrons in } \mathrm{{}^{35}S} = 35 \text{ (mass number)} - 16 \text{ (protons)} = 19 \text{ neutrons} \][/tex]
4. Compare the options given:
- Option A: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 32 protons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 35 protons. (Incorrect, both have 16 protons)
- Option B: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 protons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 protons. (Incorrect, both have 16 protons)
- Option C: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 32 neutrons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 35 neutrons. (Incorrect, [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 neutrons and [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 neutrons)
- Option D: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 neutrons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 neutrons. (Correct)
The correct comparison of the sulfur isotopes [tex]\(\mathrm{{}^{32}S}\)[/tex] and [tex]\(\mathrm{{}^{35}S}\)[/tex] is given in Option D: [tex]\(\mathrm{{}^{32}S}\)[/tex] has 16 neutrons, whereas [tex]\(\mathrm{{}^{35}S}\)[/tex] has 19 neutrons.
