# 3.67: Conservation of Mass and Energy in Nuclear Reactions

**At Grade**Created by: CK-12

**Practice**Conservation of Mass and Energy in Nuclear Reactions

If the name Albert Einstein causes your eyes to glaze over, because it makes you think of abstract theories and complex equations, remember this image of the famous physicist. He obviously had a sense of humor. More importantly, he single-handedly turned science upside down with the ideas he introduced in the early 1900s. Amazingly, those ideas have withstood the test of time as more and more evidence has been gathered to support them.

### Einstein’s Famous Equation

Einstein’s best-known equation—and possibly the best-known equation of all time—is actually very simple: E = mc^{2}

This equation is incredibly important. It changed how scientists view energy and matter, which are two of the most basic concepts in all of science. The equation shows that energy and matter are two forms of the same thing. You can listen to a recording of Einstein explaining his famous equation at this URL:

http://www.youtube.com/watch?v=CC7Sg41Bp-U

**Q**: What do the letters in Einstein’s equation stand for?

**A**: E stands for energy, m stands for mass, and c stands for the speed of light.

The speed of light is 300,000 kilometers (186,000 miles) per second, so c^{2} is a very big number. Therefore, the amount of energy in even a small mass of matter is tremendous. Suppose, for example, that you have 1 gram of matter. That’s about the mass of a paperclip. Multiplying this mass by c^{2} would yield enough energy to power 3,600 homes for a year!

### Mass and Energy in Nuclear Reactions

Einstein’s equation helps scientists understand what happens in nuclear reactions and why they produce so much energy. When the nucleus of a radioisotope undergoes fission or fusion in a nuclear reaction, it loses a tiny amount of mass. What happens to the lost mass? It isn’t really lost at all. It is converted to energy. How much energy? E = mc^{2}. The change in mass is tiny, but it results in a great deal of energy.

**Q**: In a nuclear reaction, mass decreases and energy increases. What about the laws of conservation of mass and conservation of energy? Are mass and energy not conserved in nuclear reactions? Do we need to throw out these laws when it comes to nuclear reactions?

**A**: No, the laws still apply. However, it’s more correct to say that the sum of mass and energy is always conserved in a nuclear reaction. Mass changes to energy, but the total amount of mass and energy combined remains the same.

### Summary

Einstein’s equation, E = mc^{2}, shows that matter and energy are two forms of the same thing. It also shows that there is a tremendous amount of energy (E) in a small mass (m) of matter.

- In nuclear reactions, matter changes to energy, but the total amount of mass and energy together does not change.

### Practice

Watch the short video about E = mc^{2} at the bottom of the following Web page. Then, answer the questions below.

http://curiosity.discovery.com/question/why-speed-of-light-squared

- Describe how a flashlight explains Einstein’s equation, including where the c
^{2}comes from. - Einstein argued that all matter, right down to protons, contain stored energy. Give examples of common objects that contain stored energy (called potential energy).

### Review

- Describe in words the meaning of Einstein’s equation, E = mc
^{2}. - Why is this equation so important?
- How does Einstein’s equation relate to the conservation of mass and energy in nuclear reactions?

### Image Attributions

- Explain the meaning of Einstein’s famous equation, E = mc
^{2}. - Relate Einstein’s equation to the conservation of mass and energy in nuclear reactions.