Presentation on theme: "Section 2: Mass Defect and E=mc 2. Since an atom is made of protons, neutrons, and electrons, you might expect the mass of the atom to be the same as."— Presentation transcript:
Section 2: Mass Defect and E=mc 2
Since an atom is made of protons, neutrons, and electrons, you might expect the mass of the atom to be the same as the mass of all of these combined. ◦ However, this is not always the case. Lets look at He... 2 Protons: (2 x amu) = amu 2 Neutrons: (2 x amu) = amu 2 Electrons: (2 x amu) = amu Total combined = amu
The actual atomic mass of Helium has been measured to be amu… ◦ The difference between the mass of an atom and the sum of the masses of its particles is called the mass defect. ◦ Sooooooooo where did the rest of the mass go?! According to Einstein, it was converted directly into energy!
Albert Einstein developed an equation to measure the amount of energy created when the nucleus is created from loose particles (fusion) or split apart (fission). E=mc 2 Energy (Unit = J) Δ Mass in Kg (mass of products– mass of reactants) Constant (3.00 x 10 8 m/s) Speed of light in a vacuum
Step 1: Calculate the mass of the reactants and products… ◦ U + n Ba + Kr + 2 n ◦ Mass of a neutron = amu ◦ Reactants: U (235) + n (1.0087) = amu ◦ Products: Ba (142) + Kr (92) + 2 n ( x 2) = amu ◦ Difference: – = amu
Step 2: Convert mass to Kilograms by multiplying difference in mass (amu) by x kg amu x x kg = x kg Now this number can be plugged into the equation…
Step 3: Solve for E using mass (kg) and constant (3.00 x 10 8 m/s) E=mc 2 E= (1.4447x kg)(3.00x10 8 m/s) 2 E= (1.4447x kg) 9.00x10 16 m 2 /s 2 E= x kg x m 2 /s 2 = 1.30 x J
Calculate the energy released when we split U-235 into Cs and Rb. U + n Cs+ Rb+ 2 n = amu (Reac) = amu (Prod) Difference: = amu x x kg = x kg
E=mc 2 E= (3.3066x kg)(3.00x10 8 m/s) 2 E= (3.3066x kg) 9.00x10 16 m/s E= x kg x m 2 /s 2 = 2.98 x J Uranium will release 2.98 x J of energy when it splits into Cs and Rb!
Calculate the energy released when two Hydrogen isotopes fuse. H + H He + n = 5 amu (Reactants) = amu (Products) Difference: = amu Convert to Kg: amu x x kg = x kg
E=mc 2 E= (1.4447x kg)(3.00x10 8 m/s) 2 E= (1.4447x kg) 9.00x10 16 m 2 /s 2 E= x kg x m 2 /s 2 = 1.30 x J The two hydrogen isotopes will release 1.30 x J of energy when they fuse together!