Question

What is the order of magnitude of one light year?
$\text{A}\text{. }{{10}^{15}}m$
$\text{B}\text{. }{{10}^{10}}m$
$\text{C}\text{. 9}\text{.2}\times {{10}^{15}}m$
$\text{D}\text{. }{{10}^{16}}m$

Answer 1

Hint: Light in vacuum travels at speed of $3\times {{10}^{8}}m{{s}^{-1}}$, which is the fastest. One light year is the distance that a light travels in vacuum in one year. Use the formula $\text{distance = speed }\!\!\times\!\!\text{ time}$ and find the value of one light year in meters.

Formula used: $\text{distance = speed }\!\!\times\!\!\text{ time}$

Complete step by step answer:
One light year is the distance that a light travels in vacuum in one year. Hence, light years are the unit of distance.
Let us convert one light year into metres. Since, one light year is the distance travelled by light in one year, we will use the relation between speed, distance and time i.e. $\text{distance = speed }\!\!\times\!\!\text{ time}$…….. (i).
We know that the speed of light in vacuum is equal to $3\times {{10}^{8}}m{{s}^{-1}}$.
We also know that one year is equal 365 days (not a leap year). One day is equal to 24 hours. Therefore, one year will be equal to $365\times 24hours$, which is equal to 8760 hours.
Convert 8760 hours into seconds. We know that one hour is equal to 60 minutes and one second is equal to 60 seconds. Therefore, one hours is equal to $60\times 60$ seconds. Therefore, one hour is equal to 3600 seconds. This implies that 8760 hours will be equal to $8760\times 3600$ seconds, which is equal to 31536000 seconds.
Therefore, one year is equal to 31536000 seconds, since one year is equal to 8760 hours.
Now we want to find the distance travelled by light in vacuum in one year. For that, substitute the value of time as one year and the value of speed as speed of light in vacuum.
Therefore, $\text{distance = }3\times {{10}^{8}}m{{s}^{-1}}\times 1year$ …… (ii).
We just now calculated that one year is equal to 31536000 seconds. Substitute this value of one year in seconds in equation (ii).
Therefore, $\text{distance = }3\times {{10}^{8}}m{{s}^{-1}}\times 31536000s=9.4608\times {{10}^{15}}metres\approx {{10}^{16}}m$.
Therefore, the order of magnitude of one light year is ${{10}^{16}}metres$.
So, the correct answer is “Option D”.

Note: Note that we cannot not use the unit light years in our day to day life. As you can see, one light year is such a large value of distance. Distance is measured in the units of light years only in astronomy, where they deal with objects that are millions of metres far from earth. There we cannot deal with the distance in metres and kilometres. That is why the unit light years is used.