SCI 270: On Nuclear Technology Practice Problems

## 10. Nuclear Fusion Energy

Rest masses in amu: electron or positron, 0.00055, H, 1.007825; n, 1.008665; D, 2.0140; T, 3.01605; 3He, 3.01603; 4He, 4.00260; 12C, 12.000000, 16O, 15.99491.
1. In most literature, the burning of hydrogen in stars is usually represented by the reaction:

4 1H ® 4He + 2 b+ + Q,

where Q is the energy of the reaction. This reaction focuses only on the nuclei involved. It appears as if charge is not conserved. Write the equation to show that charge is actually conserved. Also give the reaction equation for the positron. Calculate the amount of energy Q for the hydrogen burning reaction.

 Completeequation _______________________________ Subsequentreaction of b+ _______________________________ Q = _______________________________ MeV / 4He formed     = _______________________________ J / mole 4He formed Energy is releasedin the form of _______________________________

2. Here are some hypothetical fusion reactions. Starting from 6 H and 6 n, one can hypothetically make 6 D, 3 He or 1 C. On the other hand, one can make 1 C from 3 He, 6 D or 6 H + 6 n. All these are exothermic reactions. The energy released depends on the stability of the nuclides. Calculate the energy released in these reactions and take a step back to analyze the relationship of the Q's. The Q's can be expressed in terms of Q's in other reactions. The answer may not be unique, but their relationship illustrates the conservation of energy. The reason as to why certain reaction occure, but others not is hard to explain however. If you can make an energy-level diagram to show the relationship, that will be great. From the relationships, please consider other ways of evaluating the energy of reactions Q such as using binding energies or mass excesses.

Reaction Q in MeV Relathionship of Q's
6 1H1 + 6 1n ® 12C6 + QC QC = __ QC = QD + QD-C _ (t/f)
QC = QHe + QHe-C _ (t/f)
6 1H1 + 6 1n ® 6 2D + QD QD = __ QD = _____________
6 1H1 + 6 1n ® 3 4He + QHe QHe = __ QHe = _____________
6 2D1 ® 12C6 + QD-C QD-C = __ QD-C = _____________
3 4He2 ® 12C6 + QHe-C   QHe-C = __   QHe-C = _____________

3. The heat of combustion for propane, C3H8, is 2202 kJ per mole,

C3H8 + 5 O2 = 3 CO2 + H2O + 2202 J.

The molar masses of propane and oxygen are 44.1 and 32.0 g/mol respectively. Calculate the amounts of propane and oxygen required to provide 1016 J energy.

If the fusion reaction,

D + T ® 4He + n + 17.6 MeV,

is employed in a hydrogen bomb to provide 1016 J of energy, and that the stoichiometric mixture burns complete, calculate the required amounts of D2 and T2 gases.

 Propane _________________ kg; O2 _________________ kg; D2 _________________ kg; T2 _________________ kg.

4. How can neutrons released in the fusion of deuterium and tritium be utilized in either thermonuclear bombs or in controlled nuclear fusion to generate more material for fusion rather than allowing them to decay? Give the nuclear reactions in the utilization.

 _________________________________________ _________________________________________

5. Please consider these questions regarding cold fusion. However, you are not required to answer them for marking.
If the fusion induced by electrolysis were true, what chemical and physical evidences should be present? What are the possible fusion reactions? What are the products? How can the products be identified or detected?
Answers to Practice Problems 10 are available, but do your part first. Your skills are tested and they are yours forever.