# Nuclear Fusion (Worksheet)

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Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

The rest masses of key particles in nuclear fusion reactions are shown in the following table.

Rest masses (amu)
$$\beta^-$$ $$\beta^+$$ 1H n 2H 3H 3He 4He 12C 16O
0.00055 0.00055 1.007825 1.008665 2.0140 3.01605 3.01603 4.00260 12.0000 15.99491

## Q1

The "burning" of hydrogen in stars is usually represented by the reaction:

$\ce{4 ^1H \rightarrow\, ^{4}He + 2 \beta^{+} + E}$

where $$E$$ is the energy of the reaction. This reaction focuses only on the nuclei and ignore the electrons, so it appears as if charge is not conserved. Write the equation to show that addresses the charges of the species and confirms that charge is actually conserved.

Also give the reaction equation for the positron.

Calculate the amount of energy Q for the hydrogen burning reaction.

## Q2

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 E's. The E's can be expressed in terms of E'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 occur, 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 E such as using binding energies or mass excesses.

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

## Q3

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

$\ce{D + T \rightarrow ^4He + n + 17.6\, MeV}$

is employed in a hydrogen bomb to generate 1016 J of energy, and that the stoichiometric mixture "burns" complete (i.e., no excess reactants), calculate the required amounts of $$D_2$$ and $$T_2$$ gases.

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.

Please consider these questions regarding cold fusion. However, you are not required to answer them for marking.