If the velocity of light is \( 3.0 \times 10^{8} \) metres per second, calculate the distance travelled by light in a light year and express it in standard form.

Given:

Velocity of light $=3\times10^8 m/s$

Time  $= 1$ year 

To do:

We have to find the distance travelled by light in a light year.  

Solution:

Distance $=$ Speed $\times$ Time

Time $= 1$ year , 

Convert year to seconds

$1$ year $= 365$ days

$1$ year  =  $365 \times 24$ hours                    (1 day = 24 hours)

$1$ year  = $365 \times 24 \times 3600$ seconds   (1 hour = 60 min = 3600 sec ;

24 hours = 24 $\times$ 3600 sec )

$1$ year $= 31536000$ seconds ≈ $3.15 \times 10^7$ seconds

Distance travelled by light $=  3 \times 10^8 \times 3.15 \times 10^7$ m 

Distance  $=  3 \times 3.15  \times 10^8 \times 10^7$ m 

Distance  $= 9.45 \times 10^{8+7}$ m  

Distance  $=  9.45 \times 10^{15}$ m  

So, the distance traveled by light in 1 year is $9.45 \times 10^{15}$ metres. 

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Updated on: 10-Oct-2022

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