Answer :
To determine the atomic radius of oxygen given the bond length of oxygen gas, we need to follow these steps:
1. Understand the problem: The bond length in an oxygen molecule (\(O_2\)) is given as \(1.20741 \times 10^{-10}\) meters. This bond length represents the distance between the centers of the two oxygen atoms.
2. Relate bond length to atomic radius: For diatomic molecules like \(O_2\), the bond length is approximately twice the atomic radius. Therefore, the atomic radius can be calculated by dividing the bond length by 2.
3. Calculate the atomic radius:
[tex]\[ \text{Atomic Radius} = \frac{\text{Bond Length}}{2} = \frac{1.20741 \times 10^{-10} \text{ m}}{2} \][/tex]
4. Perform the division:
[tex]\[ \text{Atomic Radius} = \frac{1.20741}{2} \times 10^{-10} \text{ m} = 0.603705 \times 10^{-10} \text{ m} \][/tex]
5. Simplify the scientific notation: Write \(0.603705 \times 10^{-10}\) m in a proper scientific notation format:
[tex]\[ 6.03705 \times 10^{-11} \text{ m} \][/tex]
Hence, the atomic radius of oxygen, when written correctly in scientific notation, is \(6.03705 \times 10^{-11}\) meters.
Given the options:
- \(6 \times 10^{-11}\)
- \(6.037 \times 10^{-11}\)
- \(6.03705 \times 10^{-11}\)
- \(6.04 \times 10^{-11}\)
The correct choice is [tex]\(6.03705 \times 10^{-11}\)[/tex].
1. Understand the problem: The bond length in an oxygen molecule (\(O_2\)) is given as \(1.20741 \times 10^{-10}\) meters. This bond length represents the distance between the centers of the two oxygen atoms.
2. Relate bond length to atomic radius: For diatomic molecules like \(O_2\), the bond length is approximately twice the atomic radius. Therefore, the atomic radius can be calculated by dividing the bond length by 2.
3. Calculate the atomic radius:
[tex]\[ \text{Atomic Radius} = \frac{\text{Bond Length}}{2} = \frac{1.20741 \times 10^{-10} \text{ m}}{2} \][/tex]
4. Perform the division:
[tex]\[ \text{Atomic Radius} = \frac{1.20741}{2} \times 10^{-10} \text{ m} = 0.603705 \times 10^{-10} \text{ m} \][/tex]
5. Simplify the scientific notation: Write \(0.603705 \times 10^{-10}\) m in a proper scientific notation format:
[tex]\[ 6.03705 \times 10^{-11} \text{ m} \][/tex]
Hence, the atomic radius of oxygen, when written correctly in scientific notation, is \(6.03705 \times 10^{-11}\) meters.
Given the options:
- \(6 \times 10^{-11}\)
- \(6.037 \times 10^{-11}\)
- \(6.03705 \times 10^{-11}\)
- \(6.04 \times 10^{-11}\)
The correct choice is [tex]\(6.03705 \times 10^{-11}\)[/tex].
