Distinguish between fission and fusion - Leaving Cert Physics - Question 8 - 2006

Large temperatures are required for fusion to occur due to the repulsive forces between positively charged nuclei. The high temperatures provide sufficient kinetic energy for the nuclei to overcome the Coulomb force of repulsion and come close enough for the strong nuclear force to take effect, leading to fusion.

The equation for the nuclear reaction involving two isotopes of helium can be written as:

\text{^3He} + \text{^3He} \rightarrow \text{^4He} + 2\text{^1H}

The necessary condition for this reaction to take place on Earth is the requirement of a large initial temperature, typically in the range of millions of degrees Celsius, to provide the necessary energy for the reaction.

To calculate the energy released during the reaction, we can use the mass-energy equivalence principle:

$E = mc^2$

where:

• mass defect $m = \text{mass of reactants} - \text{mass of products}$.

Given:

• mass of reactants: $m_{^3He} = 3.846 \times 10^{-27} \text{ kg} \left(\text{for two nuclei: } 2 \times 3.846 \times 10^{-27}\right)$
• mass of products: $m_{^4He} + 2m_{^1H}$

Calculating the energy yields:

• $E = 2.8 \times 10^6 \times (2.998 \times 10^8)^2$,
• which gives approximately $E = 2.516 \times 10^{-12} ext{ J} \approx 2.52 \times 10^{-12} ext{ J}$.

Fuel: Plentiful and readily available isotopes can be used, such as deuterium from seawater.

Energy: Vast amounts of energy are released, providing a significant energy source while producing minimal waste.

Pollution: Minimal radioactive waste is produced compared to fission reactors, leading to reduced environmental impact.