The correct option is 9.461 × 10^12 km.
Explanation
A Light Year is a unit of astronomical distance, defined as the distance that light travels in a vacuum in one Julian year (365.25 days). It is primarily used to measure vast distances between stars and galaxies outside the solar system.
Calculation and Analysis:
- The speed of light in a vacuum is approximately 300,000 kilometers per second ($3 \times 10^5$ km/s).
- To derive the value of a light year, the speed is multiplied by the number of seconds in a year:
$\text{Distance} = 300,000 \text{ km/s} \times 60 \text{ s/min} \times 60 \text{ min/hr} \times 24 \text{ hr/day} \times 365.25 \text{ days}$ - The resulting value is approximately $9.461 \times 10^{12}$ km (9.46 trillion kilometers).
Analysis of Incorrect Options:
- 300,000 km: 300,000 km represents the distance light travels in one second.
- 150 million km: 150 million km represents one Astronomical Unit (AU), which is the average distance between the Earth and the Sun.
- 13.7 billion km: 13.7 billion is typically associated with the age of the universe (13.7 billion years), not the distance of a light year.
Key Takeaway:
A light year is a measure of distance, not time. It is equivalent to approximately $9.46 \times 10^{12}$ km.