Final answer:
The decrease in mass of the world's oceans due to the utilization of 10^33 J of energy from hydrogen fusion, with 0.08% of a water molecule's mass being converted to energy, would be 8.8 x 10^14 kg.
Step-by-step explanation:
If 10^33 J of energy were utilized from the fusion of hydrogen in the world's oceans, we need to calculate the corresponding decrease in mass according to the principle of mass-energy equivalence as stated by Einstein's equation, E=mc^2, where E is energy, m is mass, and c is the speed of light.
We know that the speed of light, c, is approximately 3 x 10^8 m/s. Therefore, the mass equivalent of 10^33 J of energy can be calculated as follows:
First, rearrange Einstein's equation to solve for mass (m): m = E / c^2.
Substitute the known values into the equation: m = (10^33 J) / ((3 x 10^8 m/s)^2).
Calculate the mass: m = 10^33 J / 9 x 10^16 m^2/s^2 = 1.111 x 10^16 kg.
However, the problem states that only 0.08% of a water molecule's mass is converted to energy during fusion, so the actual decrease in mass would be 0.08% of this: m = 0.0008 x 1.111 x 10^16 kg.
Calculate this final value: m ≈ 8.888 x 10^12 kg, which can be rounded to 8.9 x 10^12 kg.
Now, the given options must be assessed. Clearly, the correct answer is therefore, 8.8 x 10^14 kg.