How the Sun Works
If you wanted to go to a store and buy a light bulb as powerful as the Sun, you would have to find one that is 4 x 10^{26} watts. That's a lot of electricity!
But we know that electricity doesn't power the Sun. The only power source that could give off this much energy for billions and billions of years is nuclear fusion. In this activity, you are going to find out how many fusion reactions a second must occur to keep the Sun burning as bright as it does, and therefore how much Hydrogen fuel it takes to keep the Sun going. This is one gas tank you don't want to have to fill!

 Hydrogen fusion in the Sun occurs in three steps called the protonproton chain. You start with four Hydrogen atoms and you end up with one Helium atom. We can find the quantity of energy released in one of the fusion reactions by comparing the mass of what goes in to the mass of what comes out. Where did the mass go? Into energy! Using Einstein's massenergy relationship to find out how much energy comes out of a single fusion reaction. For data on Hydrogen, Helium, and anything else you might need use your periodic table and your reference tables. 1 u = 1.6605 x 10^{27} kg
Amount of energy released in one fusion reaction = ___________________
2. If the Sun gives off 4 x 10^{26} watts of energy, how many fusion reactions happen every second?
3. Every reaction eats up 4 Hydrogen atoms. So how much mass does the Sun fuse every second?
4. Finally, if the Sun were 2 x 10^{30} kg, how long would it take for the Sun to use all of its available mass in the fusion process?
Answer key
Question 1:
Find the mass defect in kilograms and then turn that into energy using E = mc^{2}:
4 Hydrogen atoms  1 Helium atom = mass defect (kg)
4 (1.673 x 10^{27} kg.)  1 (6.645 x 10^{27} kg.) = 0.048 x 10^{27} kg.
E = (0.048 x 10^{27} kg) (3 x 10^{8} m/s)^{2} = 4.3 x 10^{12}Joules
Amount of energy released in one fusion reaction = 4.3 x 10^{12}Joules/reac.
Question 2:
If the Sun gives off 4 x 10^{26} watts of energy, how many fusion reactions happen every second?
4 x 10^{26} Joules/second / 4.3 x 10^{12} Joules/react = 9.3 x 10^{37} reactions/second.
Question 3:
Every reaction fuses 4 Hydrogen atoms:
(9.3 x 10^{37} reactions/second) x (6.693 x 10^{27} kg/reaction) = 6.224 x 10^{11} kg/s
Question 4:
2 x 10^{30} kg / 6.224 x 10^{11} kg/s 3.213 x 10^{18} seconds = 10^{11} years!
In reality, the entire Sun is not Hydrogen and fusion only occurs in the core. So about 70% of the Sun is available for fusion, making this number smaller.
Copyright © 2002 American Museum of Natural History. All rights reserved.

More About This Resource...

This activity challenges kids to calculate how many fusion reactions a second must occur to keep the Sun burning as bright as it does.
 The activity begins with an overview that helps students grasp the amount of energy given off by the Sun by translating it into watts.
 Then, in four mathematical steps, it walks students through the calculations to determine the number of fusion reactions/second that are needed.
 An answer key is included, which spells out each calculation to help students check their answers and correct any mistakes they made.

Completion Time
Approximately 1 period

Origin
Educators Guide 
Topic
Astronomy 
Subtopic
The Sun 
Subtopic
National Science Education Standards
Grades 912:
Science as Inquiry CONTENT STANDARD A:• abilities necessary to do scientific inquiry• understanding about scientific inquiry
Physical Science CONTENT STANDARD B:
• structure of atoms• structure and properties of matter• chemical reactions• conservation of energy and increase in disorder• interactions of energy and matter
History and Nature of Science CONTENT STANDARD G:
• science as a human endeavor• nature of scientific knowledge

Learning Standard
National Science Education Standards
Grades 912:
Science as Inquiry CONTENT STANDARD A:• abilities necessary to do scientific inquiry• understanding about scientific inquiry
Physical Science CONTENT STANDARD B:
• structure of atoms• structure and properties of matter• chemical reactions• conservation of energy and increase in disorder• interactions of energy and matter
History and Nature of Science CONTENT STANDARD G:
• science as a human endeavor• nature of scientific knowledge
