Nuclear Binding Energy
The formula used to calculate the amount of energy released during the complete transformation of mass into energy is
ΔE = Δmc2
This formula can be used during radioactive decay to determine how much kinetic energy is present in either the behavior of the reactants or the products. Customarily, atomic masses are stated in atomic mass units, or amu, when given during nuclear reactions. Energies are also often given in electronvolts, eV, instead of Joules. However, virtually all the formulas require standard SI units of kg and J instead. Subsequently, here are the conversion factors to change amu to kg and eV to J:
1 amu = 1.6606 x 10-27 kg
1 eV = 1.6 x 10-19 J
Suppose you were asked to determine the energy released from the mass deficit in the reaction shown below.
where the atomic masses for the reactants and products are: The first step in answering this question would be to determine the relative masses of the reactants and then the products.
reactants
|
products
|
7
3Li = 7.01601
|
4
2He = 4.00260
|
1
1H = 1.00718
|
4
2He = 4.00260
|
8.02319 amu
|
8.00520 amu
|
The nuclear mass defect (deficit) is the difference in these two values, or 0.01799 amu. Since this additional mass was present in the reactants, it will be released as energy with the two products. This energy can be calculated with the equation E = Δmc2. Notice that the mass unit, amu, was first converted into kilograms before making this final calculation.
E = |
Δmc2 |
E =
|
0.01799(1.66 x 10-27)(3 x 108)2 |
E = |
2.59056 x 10-11 J, or
|
E =
|
16.8 MeV
|
The following graph shows a summary of when nuclear reactions "release energy." Note that both fusion and fission reactions lower the mass per nucleon until the reaction reaches the element iron which has the greatest binding energy per nucleon of 8.8 MeV. |