Final answer:
The energy produced when the sun converts 1 kg of hydrogen atoms into helium is approximately 2.5 x 10^15 joules.
Step-by-step explanation:
The energy produced when the sun converts 1 kg of hydrogen atoms into helium can be calculated by considering the mass-energy equivalence. According to the information given, the conversion of four hydrogen atoms to one helium atom results in the conversion of about 0.02862 times the mass of a proton to energy. The mass of a hydrogen atom is approximately the same as that of a proton, which is given in Appendix E. Therefore, to find the energy produced, we can multiply the mass of hydrogen converted (1 kg) by the conversion factor (0.02862 times the mass of a proton) and the speed of light squared (c^2).
Using Einstein's famous formula E = mc^2, where E is the energy, m is the mass, and c is the speed of light, we have:
E = (1 kg)(0.02862 mp)(c^2)
Substituting the value of the mass of a proton and the speed of light squared, we get:
E = (1 kg)(0.02862)(1.67 x 10^-27 kg)(3 x 10^8 m/s)^2
Simplifying the expression and calculating, we find that the energy produced is approximately 2.5 x 10^15 joules.