1. Energy-Mass Equivalence Principle By Albert Einstein

2. E = mc 2 E = total energy of a system M = total mass of the system C = speed of light If an object is not moving then: E o = m o c 2 E o is the rest energy and m o is the rest mass

3. Example: I put my sister’s 200g pet gerbil into a thermonuclear flux capacitor which converts the gerbil into pure energy. How much energy do I get out? E o = m o c 2 E o = 0.200(3.0x10 8 ) 2 E o = 1.8x10 16 J One gerbil is enough energy to power the entire country for a little while

4. Relativistic Considerations If the object is moving at relativistic speeds, then mass dilates: m =γm o So: E = mc 2 becomes E = γm o c 2

5. Relativisitic Considerations Total E is the rest E plus Ek: E = E o + E k mc 2 = m o c 2 + E k E k = mc 2 - m o c 2 E k = γm o c 2 - m o c 2 E k = m o c 2 (γ – 1)

6. Newton’s formula for E k works well: E k = ½ mv 2 But it breaks down at very high speeds. In that case, use Einstein’s version. Einstein’s formula is the same as Newton’s formula but it is harder to work with.

7. Sample Problem A 400kg car is traveling at 30m/s. Find the kinetic energy of the car using Newton’s formula and Einstein’s formula. Newton: E k = ½ mv 2 E k = ½ (400)(30) 2 E k = 1.80x10 5 J

8. Einstein: E k = m o c 2 (γ – 1) At v = 30m/s, γ = 1.000000000000005 E k = 400(3.0x10 8 ) 2 (5x10 -15 ) E k = 1.80x10 5 J Same as Newton, but a lot more tricky.

9. Nuclear Fusion Helium-3 is made of 2 protons and 1 neutron. proton mass = 1.0072764668 amu = 1.6726 x 10-27 kg proton mass = 1.0072764668 amu = 1.6726 x 10-27 kg neutron mass = 1.0086649156 amu = 1.6749 x 10-27 kg electron mass = 0.0005446623 amu = 9.1093 × 10-31 kg electron mass = 0.0005446623 amu = 9.1093 × 10-31 kg Total mass = 3.0243071738 amu

10. Nuclear Fusion Sum of parts of He-3 is 3.0243071738 amu Actual mass of He-3 is 3.0160293191 amu The Helium has less mass than its component parts! Where does the extra mass go?

11. Nuclear Fusion All elements are made of protons and neutrons etc that are bound together. Once they are bound together, they lose mass – really they lose energy. The energy lost is called the “binding energy”. To split the atoms apart, you’ll need to inject this energy back into the atom.

12. The binding energy of He-3 is: 3.0243071738 amu - 3.0160293191 amu = 0.0082778547 amu This energy is given off as a gamma ray. 2P + 1N  He 3 + γ The fusion of hydrogen to make helium produces energy. This is the process that makes the sun hot and bright.

13. Nuclear Fission Fission is the reverse process of fusion. Splitting Helium takes energy, so it is not a useful process. As elements get heavier, it takes more and more energy to keep them together. Some elements are too massive to stay in one piece, so they naturally fall apart. These are radioactive elements.

14. Uranium is one of these heavy elements. It has 235 nucleons (protons and neutrons) and readily falls apart. Unlike Helium, Uranium takes energy to keep it together. When uranium 235 fissions, it splits into Krypton, Barium and 3 neutrons. It also releases mass in the form of a gamma ray. U  Kr + Ba + 3n + γ This process is called nuclear fission.