In astrophysics, one light year is the distance that light travels in vacuum in one year. Numerically, one light year is approximately equal to which of the following orders of magnitude in metres?

Introduction / Context:
In astronomy, distances between stars and galaxies are enormous, so everyday units like kilometre or metre are not convenient. The light year is a commonly used astronomical distance unit defined as the distance that light travels in vacuum in one year. This question tests your familiarity with the approximate size of a light year expressed in metres using powers of ten notation.

Given Data / Assumptions:

• Light travels in vacuum at a speed of approximately 3 * 10^8 m/s.
• One year is taken as about 365 days for the purpose of order of magnitude calculations.
• We want the approximate distance in metres that light covers in one year.
• Options are given in the form 10^12 m, 10^16 m, 10^11 m and 10^13 m.

Concept / Approach:
Distance is equal to speed multiplied by time. For a light year, we multiply the speed of light by the number of seconds in one year. While a precise value includes leap years and more precise timekeeping, for competitive exams an order of magnitude estimate is sufficient. The important point is that the resulting distance is closer to 10^16 m than to any of the smaller powers of ten listed. The commonly quoted value is about 9.46 * 10^15 m, which is closest to 10^16 m when rounded to one significant figure.

Step-by-Step Solution:
Step 1: Write the speed of light in vacuum as c approximately equal to 3 * 10^8 m/s. Step 2: Estimate the number of seconds in one year: 1 year approximately equals 365 days, each day has 24 hours, each hour 3600 seconds. Step 3: Compute time in seconds: t approximately equal to 365 * 24 * 3600. Step 4: For order of magnitude, 365 is roughly 3.65 * 10^2, 24 is about 2.4 * 10^1 and 3600 is 3.6 * 10^3. Step 5: Multiply: t approximately equal to (3.65 * 2.4 * 3.6) * 10^(2+1+3) seconds. Step 6: The numeric product 3.65 * 2.4 * 3.6 is roughly between 30 and 35, so t is about 3 * 10^1 * 10^6 equal to 3 * 10^7 seconds, which matches the known rough value of about 3.15 * 10^7 seconds per year. Step 7: Distance for one light year is then d = c * t approximately equal to (3 * 10^8) * (3 * 10^7) equal to 9 * 10^15 m, which is commonly rounded to about 10^16 m.

Verification / Alternative check:
Standard astronomy references usually quote 1 light year as approximately 9.46 * 10^15 m. When writing distances in a simple multiple choice format with approximate orders of magnitude, this is closest to 10^16 m. The other options 10^11 m, 10^12 m and 10^13 m are far too small; 10^13 m, for example, is only one thousandth of a light year. Distances within our solar system, such as the separation between the Sun and Pluto, are measured in astronomical units, which are much smaller than a light year. This confirms that the only reasonable choice for the distance of one light year is about 10^16 m.

Why Other Options Are Wrong:
10^11 m is only one hundred billion metres, which is far less than the distance light travels in a year and is closer to planetary scale distances. 10^12 m is one trillion metres, still many orders of magnitude smaller than a light year. 10^13 m is ten trillion metres, which is about one thousandth of a light year and is still too small.

Common Pitfalls:
Students sometimes underestimate astronomical distances because powers of ten can be confusing. Another mistake is confusing light year with time, thinking it is a measure of time rather than distance. Always remember that a light year is a unit of distance defined by how far light travels in one year. Associating the approximate numeric value 10^16 m with one light year helps in answering many astronomy questions quickly.

Final Answer:
One light year is approximately equal to a distance of order 10^16 m.