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66. The distance between the centers of the two oxygen atoms in an oxygen molecule is \( 1.21 \times 10^{.3} \mathrm{~cm} \). What is this distance in inches?

Ask by Cook Lane. in the United States
Jan 25,2025

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Answer

The distance is approximately \(4.8 \times 10^{-9}\) inches.

Solution

To convert the distance between the centers of the two oxygen atoms in an oxygen molecule from centimeters (cm) to inches (in), follow these steps: 1. **Understand the Given Value:** The distance is given as \( 1.21 \times 10^{-8} \) cm. (Assuming the exponent is \(-8\) based on typical bond lengths.) 2. **Conversion Factor:** \( 1 \text{ inch} = 2.54 \text{ cm} \) 3. **Perform the Conversion:** \[ \text{Distance in inches} = \frac{1.21 \times 10^{-8} \text{ cm}}{2.54 \text{ cm/in}} \] \[ \text{Distance in inches} \approx 4.764 \times 10^{-9} \text{ in} \] Rounding to two significant figures: \[ \text{Distance in inches} \approx 4.8 \times 10^{-9} \text{ in} \] **Final Answer:** The distance is approximately 4.8 × 10⁻⁹ inches.

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To convert the distance between the centers of the two oxygen atoms from centimeters to inches, use the conversion factor where 1 inch is equal to 2.54 centimeters. So, to convert \( 1.21 \times 10^{-.3} \) cm to inches: \[ \text{Distance in inches} = \frac{1.21 \times 10^{-.3}}{2.54} \approx 0.000476 inches. \] Wow! That’s incredibly small, highlighting just how tiny molecules are. It’s astonishing to think that this minuscule measurement is key to the very structure of the oxygen we breathe! When dealing with measurements like this, it’s easy to make common mistakes. Always double-check your conversion factors and ensure that you’re consistent with your units throughout the calculations. And remember, using scientific notation can help handle vastly different scales efficiently.

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