Question

Imagine that you see an enormous explosion out in space. This explosion puts out a total energy of 10^44 J, and lasts for a week. Detailed observations show that this explosion did not blast any gas into space, even though there was plenty of hydrogen close to the exploding object. What is the minimum possible mass of the thing that exploded (in kg)? You may assume that G=6.67×10^−11N m^2 kg^−2 , c=3.0×10^8m s^−1 , mp=1.67×10^−27kg , h=6.63×10^−34m^2 kg s^−1 and σT=6.7×10^−29m^2. You may also assume that the explosion had a constant brightness throughout the week.

a) 2.4 × 10^31 kg
b) 1.8 × 10^31 kg
c) 3.6 × 10^31 kg
d) 4.2 × 10^31 kg

Answer 1

The minimum possible mass of the object that exploded is approximately 2.24 × 10^31 kg.

Step-by-step explanation:

To find the minimum possible mass of the object that exploded, we can use the equation E = mc^2, where E is the energy released, m is the mass, and c is the speed of light. Rearranging the equation to solve for mass, we have m = E / c^2. Plugging in the given values, we get:

m = (1.00 × 10^44 J) / (3.0 × 10^8 m/s)^2

Calculating this, we find that the minimum possible mass of the object that exploded is approximately 2.24 × 10^31 kg. Therefore, the correct answer is option a) 2.4 × 10^31 kg.