Earth is about 28,000 light years from the center of the Milky Way Galaxy.If a supernova explosion occurred approximately 14,000 light years away from us and released 2.0 $\times$ 10⁴⁶ J of energy in a sudden burst of light,how much energy would enter one of your pupils? Assume the diameter of a pupil to be about 4 mm.(For comparison,our Sun radiates approximately 4 $\times$ 10²⁶ J/s.) A)1.1 J B)3.0 $\times$ 10²³ J C)3.5 J D)4.6 J E)2.2 J

Question

Quizplus · Accepted Answer

The amount of energy that would enter one of your pupils can be calculated by using the formula for the area of a circle, A = πr², where r is the radius of the pupil (2 mm) and π is approximately 3.14. 
A = π(2 mm)² = 12.6 mm² 
Converting this area to meters: 
A = (12.6 mm²)(1 m/1000 mm)² = 1.26 x 10^-8 m² 
The energy that would enter one of your pupils can be calculated by dividing the total energy released by the supernova by the surface area of a sphere with a radius of 14,000 light years (the distance from us to the supernova): 
E = (2.0 x 10^46 J)/(4π(14,000 light years x 9.46 x 10^15 m/light year)²) 
E = 1.1 J 
Therefore, the best answer is A) 1.1 J.

Earth Is About 28,000 Light Years from the Center of the Milky