Answer:
635 years old
Explanation:
The light reaching the earth from the sun will travel at a speed called the speed of light, and this has a universal value of 3 × 10⁸ m/s. Bearing this in mind, let us calculate the age of the light reaching the Earth from the sun:
Distance of star from Earth = 6.1 × 10⁸m
Speed of light = 3 × 10⁸ m/s
We have distance and speed, let us calculate the time of travel of the light from the star to the earth.
Distance = speed × time
6.1 × 10⁸ = 3 × 10⁸ × time
[tex]time = \frac{6.1 \times 10^{18}}{3 \times 10^8}[/tex]
In order to do the division above, we will divide the whole numbers normally, then we will apply the law of indices to the power that says:
Xᵃ ÷ Xᵇ = X⁽ᵃ⁻ᵇ⁾
[tex]\therefore time = \frac{6.1 \times 10^{18}}{3 \times 10^8}\\= \frac{2.03 \times 10^{(18-8)}}{1} \\= 2.03 \times 10^{10}}\ seconds[/tex]
Next, we are told that there are 3.2 × 10⁷ seconds in a year.
∴ The number of years travelled by the light from the star:
[tex]3.2\ \times 10^7\ seconds = 1\ year\\1\ second = \frac{1}{3.2\ \times 10^7} \\\therefore 2.03 \times 10^{10}\ seconds = \frac{2.03 \times 10^{10}}{3.2\ \times 10^7}[/tex]
please note that:
2.03 × 10¹⁰ = 20300000000
3.2 × 10⁷ = 32000000
[tex]\therefore \frac{2.03 \times 10^{10}}{3.2\ \times 10^7}\\= \frac{20300000000}{32000000} \\\\= \frac{20300}{32} \\= 634.347\ years\\[/tex]
The closest answer in the option is 635 years, and we are short of this by some points due probably to approximations in the calculation.
