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.

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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!