Which of the following practical units of length is not correct?

Options

A. 1 fermi = `10^(-15)`m
B. 1 astronomical unit = `1.496xx10^(11)`m
C. 1 parsec = 3.26 light year
D. 1 light year = `9.46xx10^(12)`m

Answer

To determine which of the following practical units of length is not correct, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding the Units**:
- We need to evaluate the correctness of the given units of length.

2. **Option 1: 1 femtometer = 10^-15 meters**:
- A femtometer (fm) is indeed defined as \(10^{-15}\) meters.
- **Conclusion**: This option is correct.

3. **Option 2: 1 astronomical unit (AU) = 1.496 x 10^11 meters**:
- An astronomical unit is the average distance from the Earth to the Sun, which is approximately \(1.496 \times 10^{11}\) meters.
- **Conclusion**: This option is correct.

4. **Option 3: 1 parsec = 3.26 light years**:
- A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond. It is approximately equal to 3.26 light years.
- **Conclusion**: This option is correct.

5. **Option 4: 1 light year = 9.46 x 10^12 meters**:
- A light year is the distance that light travels in one year. To calculate this:
- The speed of light \(c\) is approximately \(3 \times 10^8\) meters/second.
- The number of seconds in one year is calculated as follows:
- 1 year = 365 days
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- Therefore, the total number of seconds in a year = \(365 \times 24 \times 60 \times 60 = 31,536,000\) seconds.
- Now, calculating the distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 3 \times 10^8 \, \text{m/s} \times 31,536,000 \, \text{s} \approx 9.46 \times 10^{15} \, \text{meters}. \]
- **Conclusion**: The correct value is \(9.46 \times 10^{15}\) meters, not \(9.46 \times 10^{12}\) meters.

6. **Final Conclusion**:
- The incorrect option is **Option 4**: 1 light year = \(9.46 \times 10^{12}\) meters.