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The Sun produces energy at a rate of $4.00 \times 10^{26} \mathrm{w}$ by the fusion of hydrogen. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the Sun is 90.0$\%$ . hydrogen and half of this can undergo fusion before the Sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the Sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?

Hence, total mass of hydrogen taking part in this reaction is$$m_{t}=\left(9.50 \times 10^{37}\right)\left(6.68 \times 10^{-27} \mathrm{kg}\right)=6.35 \times 10^{11} \mathrm{kg}$$Hence, $6.35 \times 10^{11} \mathrm{kg}$ of hydrogen undergo fusion reaction each second.Hence, the fusion reaction will continue for $4.47 \times 10^{10}$ years.Hence, the total fraction of mass used is$$\frac{\left(6.26 \times 10^{27}\right)}{\left(1.99 \times 10^{30} \mathrm{kg}\right)}=3.14 \times 10^{-3}$$Sun will have lost $3.14 \times 10^{-3}$ fraction of its mass.

Physics 103

Chapter 28

Special Relativity

Relativity

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well in fusion reaction off, son, full proton fuses together to form an elf. A particle. And we know that the moss off a proton, um, the most of Coppertone. Rather, the rest must energy of a proton is given by moss off Crotone Time C square a muscle, bro. Don't Time C square is equal to 9 38 point cream 1,000,000 electron Walt, and similarly, the wrist Most energy of an alpha particle is muscle for particle time C square and muscle filled in for particle time. C square is a 3726 point mine 1,000,000 electron won't on. The difference in the reaction is given by Delta M C Square, Uh, which is four times more self proton minus muscle fell for particles and therefore Delta M C square is equal to for into, um, here we have ah mine. 38 mine 30 eight, um, 9 38 point pre 1,000,000 electron Walt minus but 3000 726.9 1,000,000 electron world. And did. For Delta M C square is equal to 4.21 multiplied by pretend to the power minus 12. Jules. Yeah, no months off. One hydrogen atom is mass off. One hydrogen atom is equal to 1.67 Multiply, bro. I tend to the collar minus 27 kilogram enhancing. One reaction. The total number of hydrogen required is, let's say I am one and it's equal to 6.68 multiplied by 10 to the power of minus 27 kilogram and some produces, um, some party, you see. So for 0.0 multiplied by 10 to the power 26 jewels off energy in one second in one second on the total number of reaction. Knockers in one second is given by an and musical to 4.0 Multiply by 10 to the power 26 divided by 4.21 Multiply by 10 to the power minus 12 and dividing the two numbers. We get 9.5 serial multiply by 10 to the power 27. Hence the total muscle hydrogen. Taking part in this reaction is uh, uh, let's say total mass off hydrogen is empty and it's equal to 9.50 multiplied by 10 $30. 37 hint 06568 multiplied by 10 to the dollar minus 27 and most of blindly to numbers. We get 6.35 multiplied by 10 to the power 11 kilogram. So the total muscle if I'd written taking part in this reaction is 6.3 by multiply by 10 to devour 11 kilogram on total months off, son is given well. Marcel's son is equal to 1.99 Multiply by 10 to the power particular brands and total marceau for hydrogen in son. Well, a total mass off hydrogen in son Marcel. Fight region is equal to 90% off Marcel son. So muscle hydrogen in sun is equal to 90% off the moss off this son. And let's simply finest well 90% of 0.90 Um, multiply by muscles and his 1.99 Multiply by 10 to the power particular graham and multiplying the two numbers. Muscle hydrogen, uh, in sun is equaled 1.79 multiply by 10 to the power 30 kilogram. So the total amount of hydrogen date will take part in the future. Reaction, Uh, a total amount off hydrogen. It will take part in the fusion reaction is he called to one divided by two into 1.79 Multiply by 10 to the forward 30 and it's equal to 8.95 multiplied by, uh, 10 to the power 29 kilogram s o. The total time the fusion reaction can continue is so T is equal to 8.95 months of life by 10 to the power 29 divided by 6.35 multiplied by tentative. Our 11 men, This gives us four point for seven multiplied by 10 to the power 10 years. The total time the fusion reaction can continue is 4.47 multiplied by 10 to the power 10 years on. Right? Well, uh, son is losing mass. A son losing mess per second is delta empty equals 4.0 multiplied by 10 to the power 26. Divided by, uh, C Square c is three multiplied attempt to devour eight, and we have squared on dividing the two numbers we have for point for four. Multiply by 10 to the power nine, uh, kilogram. All right, So in time T is equal to one point forward one. Multiply by 10 to the power 18 seconds, son would lose. Uh, delta. Mm, uh, is equal. Do for point for four. Multiply by 10 to the power nine into 1.41 multiplied by 10 to the power 18 and don't m is equal to six point to a six multiplied by 10 to the power 27 20 seven. That's the total destruction of moss used is total fraction off. Moss used is 6.26 multiplied by 10 to the power 27 divided by 1.99 Multiply by 10 to the dollar. 30 and this is able to 3.14 Multiply by 10 to the power minus treat. So son will have lost ah, 3.14 multiply by 10 to the power minus three fraction off It's a mess.

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