The correct option is 1 and 3 only.
Explanation
A Light Year is a unit of astronomical distance, not time. It represents the distance that light travels in a vacuum in one Julian year (365.25 days). It is primarily used to measure distances to stars and other galaxies.
Statement-wise Analysis
- Statement 1 is Correct: A light year is defined as the distance a beam of light travels in a single Earth year. Since the speed of light is constant in a vacuum, this provides a consistent standard for measuring vast interstellar distances.
- Statement 2 is Incorrect: The speed of light is approximately $3 \times 10^5$ km/s.
Calculating the distance:
$$ \text{Distance} = \text{Speed} \times \text{Time} $$
$$ 1 \text{ Light Year} = 299,792 \text{ km/s} \times (365.25 \times 24 \times 60 \times 60) \text{ seconds} $$
$$ 1 \text{ Light Year} \approx 9.46 \times 10^{12} \text{ km} $$
The statement incorrectly cites the value as $9.461 \times 10^{10}$ km. - Statement 3 is Correct: The mean distance between the Sun and the Earth is approximately 149.6 million kilometers (1 Astronomical Unit). Light travels at roughly 300,000 km/s.
$$ \text{Time taken} = \frac{149,600,000}{300,000} \approx 499 \text{ seconds} $$
Converting seconds to minutes: $499 / 60 \approx 8.31$ minutes. Thus, the distance is about 8.311 light minutes.
Key Takeaway: A light year is a unit of distance equivalent to approximately 9.46 trillion kilometers ($9.46 \times 10^{12}$ km). The Sun is approximately 8.3 light minutes away from Earth.