Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion. Energy is released during nuclear fusion because the total binding energy of the resulting nucleus is greater than the binding energy of the individual nuclei before the reaction. When two lighter nuclei fuse, the mass of the resulting nucleus is less than the sum of the masses of the two original nuclei. This mass difference, known as the mass defect, is converted into energy according to Einstein's equation, $E=mc^2$. This process releases energy, as the greater binding energy of the product nucleus means that it is more stable than the separate nuclei, thus resulting in a net release of energy.

A-Level AQA Physics Radioactive Decay: Explain, in terms of binding ene

Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion - AQA - A-Level Physics - Question 6 - 2021 - Paper 2

Question 6

Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion. Energy is released during nuclear fusion because the total b... show full transcript

Worked Solution & Example Answer:Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion - AQA - A-Level Physics - Question 6 - 2021 - Paper 2

Step 1

0 6 . 2 Calculate, in J, the energy released when this reaction occurs.

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Answer

To calculate the energy released during the fusion reaction of $rac{3}{2}He$ and $rac{17}{8}O$ to form $rac{20}{10}Ne$ , we first determine the mass defect, ( \Delta m ).

Using the mass values provided:

Mass of $rac{3}{2}He$ : 3.01603 u
Mass of $rac{17}{8}O$ : 16.99913 u
Mass of $rac{20}{10}Ne$ : 19.99244 u

We calculate the total mass before reaction: $\text{Total mass} = 3.01603 + 16.99913 = 20.01516 \text{ u}$

Now, calculating the mass defect: $\Delta m = 20.01516 - 19.99244 = 0.02272 \text{ u}$

We then convert this mass defect into energy using the conversion factor, 1 u = 931.5 MeV: $E = \Delta m c^2 = 0.02272 \times 931.5 \text{ MeV} = 21.16 \text{ MeV}$

Since 1 MeV = 1.6 x $10^{-13}$ J, we find: $E = 21.16 \times 1.6 \times 10^{-13} = 3.386\times 10^{-12} \text{ J}$

Therefore, the energy released when this reaction occurs is approximately $3.39 \times 10^{-12}$ J.

Step 2

0 6 . 4 Discuss, for this star, how these properties affect the rate of fusion of $\frac{34}{16}S$ with $\frac{3}{2}He$ compared to the rate of fusion of $\frac{17}{8}O$ with $\frac{3}{2}He$.

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Answer

The fusion of $\frac{34}{16}S$ with $\frac{3}{2}He$ is affected by several properties. One significant factor is the larger mass and nuclear charge of sulfur, which leads to a greater electrostatic repulsion due to the positive charges on the nuclei.

This increased repulsion means that a higher kinetic energy will be required to overcome this barrier, thus slowing down the rate of fusion reactions involving $\frac{34}{16}S$ .

In contrast, when $\frac{17}{8}O$ fuses with $\frac{3}{2}He$ , the mass and charge are lower, resulting in less electrostatic repulsion and a higher probability of fusion occurring at the same temperature. Therefore, the fusion of $\frac{17}{8}O$ with $\frac{3}{2}He$ will occur at a faster rate compared to the fusion with $\frac{34}{16}S$ .

Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion - AQA - A-Level Physics - Question 6 - 2021 - Paper 2

Worked Solution & Example Answer:Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion - AQA - A-Level Physics - Question 6 - 2021 - Paper 2

0 6 . 2 Calculate, in J, the energy released when this reaction occurs.

0 6 . 4 Discuss, for this star, how these properties affect the rate of fusion of $\frac{34}{16}S$ with $\frac{3}{2}He$ compared to the rate of fusion of $\frac{17}{8}O$ with $\frac{3}{2}He$.

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