PRINCIPLES OF NAVAL ENGINEERING 



As stated previously, naturally radioactive 

 isotopes decay bythe emission of alpha particles, 

 beta particles, gamma rays, or a combination 

 thereof. In the case of induced nuclear reactions 

 there are many other phenomena which may 

 occur, including fission and the emission of 

 neutrons, positrons, nutrions, and other forms 

 of energy.^ 



CONSERVATION OF MASS- 

 AND ENERGY 



The conservation of energy is discussed in 

 chapter 8 of this text. It now becomes necessary 

 to consider mass and energy as two phases of the 

 same principle. In so doing, the law of conserva- 

 tion becomes: 



(mass + energy) before = 

 (mass + energy) after. 



Fundamental to the above and to the entire 

 subject of nuclear power is Einstein's mass- 

 energy equation where the following relation 

 holds: 



mC 



where 



E = energy in ergs, 

 M = mass in grams, 

 C = velocity of light 



(3 X 10^° cm/sec) 



Mass and energy are not conserved separa- 

 tely but can be converted into each other. 



Several units and conversion factors which 

 have become conventional to the field of nuclear 

 engineering are listed below. 



1 amu (atomic mass unit = 1/16 of an oxy- 

 gen atom (by def- 

 inition) 



1 amu 



1.49 X 10 

 1.66 X 10 

 931 Mev 

 1.415 X 10 



24 



erg 



gm 

 13 



Btu 



NUCLEAR ENERGY SOURCE 



It was previously stated that the atomic 

 mass number is the total number of nucleons 

 within the nucleus. It can also be said that 

 the atomic mass number is the nearest integer 

 (as found by experiment) to the actual mass of 

 an isotope. In nuclear equations, the entire 

 mass must be accounted for; therefore the actual 

 mass must be considered. 



The atomic mass of any isotope is somewhat 

 less than indicated by the sum of the individual 

 masses of the protons, neutrons, and orbital 

 electrons which are the components of that 

 isotope. This difference is termed mass defect: 

 it is equivalent to the binding energy of the 

 nucleus. Binding energy may be defined as the 

 amount of energy which was released when a 

 nucleus was formed from its component parts. 



The binding energy of any isotope may be 

 found, as in the following example of copper 

 (ggCu"^) which contains 34 neutrons, 29 pro- 

 tons, and 29 electrons. Using the values given 

 in figure 24-2 we find: 



34 X 1.00894 = 

 29 X 1.00785 = 

 29 X 0.00055 = 



34.30496 amu 



29.21982 amu 



0.01595 amu 



Total of component masses 

 Less actual mass of atom 

 Mass defect 



= 63.54073 amu 

 = 62.9298 amu 

 = 0.61093 amu 



1 ev (electron-volt = the energy acquired by 

 an electron as it moves 

 through a potential dif- 

 ference of 1 volt 

 1 Mev (million electron- 

 volts) 



= 1.52 X 10-l6Btu 



Converting to energy, we find: 



= lO^ev 



For detailed information on nuclear particles, refer 

 to Samuel Glasstone, Sourcebook on Atomic Energy 

 (2d ed.; Princeton: D. Van Nostrand Company, Inc., 

 1958). 



931 Mev/amu x 0.61093 

 Mev, or 560.8 + 63 = 



amu = 568.77583 

 8.9 Mev/nucleon 



The relationship between mass number and 

 the average binding energy per nucleon is 

 shown in figure 24-5. 



Since binding energy was released when a 

 nucleus was formed from its component parts, 

 it is necessary to add energy to separate a 

 nucleus. In the fissioning of uranium 235, the 

 additional energy is supplied by bombarding the 

 fissionable fuel with neutrons. The fissionable 

 material absorbs a neutron and is converted 



618 



