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Radioactivity (A-level only)

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Question 32

During carbon burning in a massive star, two carbon-12 nuclei fuse to form a neon-20 nucleus and a helium-4 nucleus. The equation for this reaction is:

612C+612C→1020Ne+24He ^{12}_{6}\text{C} + ^{12}_{6}\text{C} \rightarrow ^{20}_{10}\text{Ne} + ^{4}_{2}\text{He} 612​C+612​C→1020​Ne+24​He

Data for these nuclei are given in the table below:

NucleusMass / u
612C^{12}_{6}\text{C}612​C12.0000012.0000012.00000
1020Ne^{20}_{10}\text{Ne}1020​Ne19.9924419.9924419.99244
24He^{4}_{2}\text{He}24​He4.002604.002604.00260

Constants:

  • Unified atomic mass unit, 1 u=1.661×10−27 kg1\text{ u} = 1.661 \times 10^{-27}\text{ kg}1 u=1.661×10−27 kg
  • Speed of light, c=3.00×108 m s−1c = 3.00 \times 10^8\text{ m s}^{-1}c=3.00×108 m s−1
  • Permittivity of free space, ε0=8.85×10−12 F m−1\varepsilon_0 = 8.85 \times 10^{-12}\text{ F m}^{-1}ε0​=8.85×10−12 F m−1
  • Elementary charge, e=1.60×10−19 Ce = 1.60 \times 10^{-19}\text{ C}e=1.60×10−19 C
a.

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

[3]
b.

One model of nuclear fusion suggests that fusion happens when nuclei touch. Initially, the two carbon nuclei are separated so that the electrostatic force between them is negligible. They move towards each other until they fuse. Fusion occurs when their centres are separated by a distance of 5.4×10−15 m5.4 \times 10^{-15}\text{ m}5.4×10−15 m. Calculate the total change in electrostatic potential energy, in J, between the initial positions and final positions of the nuclei.

[4]

Radioactivity (A-level only) Questions

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