Nuclear Fusion: The Power Behind Stars
Deuterium-Tritium Fusion
- Consider the fusion of deuterium ($ ^2\text{H} $) and tritium ($ ^3\text{H} $): $$^2\text{H} + ^3\text{H} \rightarrow ^4\text{He} + ^1\text{n}$$
- In this reaction, a helium nucleus ($ ^4\text{He} $) and a neutron ($ ^1\text{n} $) are produced.
- The mass of the reactants is slightly greater than the mass of the products, and this mass difference ($ \Delta m $) is converted into energy: $$Q = \Delta m c^2$$
- For this reaction, the energy released is approximately 17.6 MeV (million electron volts) per fusion event, an immense amount of energy at the atomic scale.
What is the role of the mass defect in determining the energy released during nuclear fusion?
Calculate the energy released in the reaction $^2\text{H} + ^3\text{H} \rightarrow ^4\text{He} + ^1\text{n}$, given the following atomic masses:
- $^2\text{H}$: 2.014102 u
- $^3\text{H}$: 3.016049 u
- $^4\text{He}$: 4.002602 u
- $^1\text{n}$: 1.008665 u
Solution
- The mass defect is: $$\Delta m = (2.014102 + 3.016049) - (4.002602 + 1.008665)$$ $$ = 0.018884 , \text{u}$$
- Convert this mass into energy using $1 \, \text{u} = 931.5 \, \text{MeV c}^{-2}$: $$Q = \Delta m c^2 $$ $$= 0.018884 \times 931.5 = 17.6 \, \text{MeV}$$
Conditions for Fusion to Occur
Fusion requires extreme conditions to overcome the Coulomb repulsion between positively charged nuclei. Let’s break down the three key conditions:
High Temperature
- At high temperatures (millions of kelvin), nuclei move at very high speeds.
- This increases the likelihood that they will collide with enough energy to overcome the repulsive electrostatic force between them.
In stars, core temperatures often exceed 10 million K, making fusion possible.
High Density
A high density of nuclei ensures that there are enough collisions happening per second to sustain a chain of fusion reactions.
ExampleIn stars, the core is incredibly dense, with billions of particles packed into a small volume.
Confinement Time
The conditions of high temperature and density must be maintained for a sufficiently long time to allow significant fusion to occur.
ExampleIn stars, gravitational pressure ensures that the core remains stable and confined.
Common Mistake- Many students think high temperature alone is enough for fusion.
- However, without high density and confinement, the nuclei would simply fly apart after collisions, preventing sustained fusion.
High Pressure
- High pressure plays a crucial role in fusion by forcing nuclei closer together, increasing the probability of collisions.
