What is the energy comparison between a gamma ray burst and vaporizing the sun?

[hobobobo]

Homework Statement

a) A back-of-the-envelope calculation shows that in about 120 seconds the gamma ray burst released a total energy of about
10^48 Joule. How does this compare to the total energy that would be released by instantly vaporizing our sun into pure energy?
(The sun's mass is about 3x10^30 kg).

b) How far away would one have to be from the gamma ray burst in order
for the average power from it (over the first 120 seconds) to be equivalent to the average power from the sun's radiation at the
earth (a quantity known as the solar constant, and which has a numerical value of about 1300 Wattëm2). Give your answer in
light years.


Ok I thought about this question and since they gave us the mass of the sun, so I was wondering if I can find E from E=mc^2. Sorry my math and physics skills are not that great. Thanx!^^

 

[Dick]

Yes, you find it from E=mc^2.

 

[hobobobo]

So how would I approach part b then?

 

[Snazzy]

You know that the intensity of the sun's light is 1300 W/m^2. I = P / (4pi r^2).

You want the intensity of the light of the GRB to be the same.

 

[hobobobo]

So do I sub in 1300 into I to find P? I don't really understand how to approach this question.

 

[Snazzy]

You want the star's intensity at the surface of the Earth to be 1300 W/m^2. You know the power of the star, you want to calculate how far it would have to be so that its intensity is 1300 W/m^2.

 

[hobobobo]

ok so I get it now. we want the intensity to be on the surface of Earth and the equation you showed me will that find it?

 

[Snazzy]

No, we don't want the intensity, we want r. We're given intensity.

 

[hobobobo]

oh I see sorry about all this I never seen that equation before. One last thing what does the capital P stand for and it says to give answer in light years

 

[hobobobo]

nvm lol I got it