Nuclear fission reactors are used as an energy source in many parts of the world, but it is only recently that the use of nuclear fusion as a possible power source is achieving some encouraging results - Leaving Cert Physics - Question 8 - 2012

Fusion offers several advantages over fission:

1. Fuel Abundance: Fusion fuel sources, such as deuterium, are more abundant than uranium. Deuterium can be extracted from water, making it widely available.
2. Less Radioactive Waste: The byproducts of fusion reactions are generally less harmful and produce significantly less long-lived radioactive waste compared to fission, which creates hazardous waste products.

To calculate the energy produced in the fusion of deuterium and tritium, we use the mass-energy equivalence principle. The reactants are:

• Deuterium (²H): Mass = 2.014102 u
• Tritium (³H): Mass = 3.016049 u
• Helium (⁴He): Mass = 4.002603 u
• Neutron (n): Mass = 1.008665 u

We sum the masses of the reactants:

$ext{Total mass of reactants} = 2.014102 + 3.016049 = 5.030151 \, u$

The mass of products:

$ext{Total mass of products} = 4.002603 + 1.008665 = 5.011268 \, u$

Now, the mass defect (mass lost) is:

$\Delta m = 5.030151 \, u - 5.011268 \, u = 0.018883 \, u$

Using Einstein's equation $E = mc^2$, where 1 u corresponds to 931 MeV, the energy produced is:

$E = 0.018883 \, u \times 931 \, MeV/u = 17.59 \, MeV$

The force of repulsion between two positively charged nuclei can be calculated using Coulomb's law:

$F = \frac{k \cdot |q_1 q_2|}{r^2}$

Where:

• $k = 8.99 \times 10^9 \, N m^2/C^2$
• $q_1$ and $q_2$ are the charges of the deuterium and tritium nuclei, each having a charge of approximately +1e, which is $1.602 \times 10^{-19} C$.
• Distance, $r = 2 \times 10^{-3} \, m$

Now substituting the values, we have:

$F = \frac{(8.99 \times 10^9) \cdot (1.602 \times 10^{-19})^2}{(2 \times 10^{-3})^2} \\ = 576.60 \, N$

Fusion requires extremely high temperatures (millions of degrees Celsius) to provide the necessary energy for overcoming the electrostatic repulsion between positively charged atomic nuclei. At these high temperatures, particles move at sufficiently high speeds for collisions to occur with enough force for fusion to take place. In essence, the kinetic energy of the particles at high temperatures is vital for achieving the conditions necessary for fusion.