In a laboratory experiment a deuterium–tritium (D–T) plasma is to be heated so that…

PHYSICS · Multi-part · CBSE · Physics · Nuclei · Nuclei

Problem

In a laboratory experiment a deuterium–tritium (D–T) plasma is to be heated so that the average kinetic energy of the nuclei is just sufficient to overcome their mutual electrostatic repulsion at contact. Take the following data: • Charge on proton: e=1.6×10−19 Ce = 1.6\times10^{-19}\,\text{C} • Boltzmann constant: k=1.38×10−23 J K−1k = 1.38\times10^{-23}\,\text{J\,K}^{-1} • Vacuum permittivity: ε0=8.85×10−12 C2 N−1 m−2\varepsilon_0 = 8.85\times10^{-12}\,\text{C}^2\,\text{N}^{-1}\,\text{m}^{-2} • Nuclear radius parameter: r0=1.2 fmr_0 = 1.2\,\text{fm} • Mass numbers: AD=2A_{\mathrm D}=2, AT=3A_{\mathrm T}=3 (Use 1 fm=10−15 m1\,\text{fm}=10^{-15}\,\text{m}.) (i) Estimate the distance between the centres of the two nuclei when they are just in contact. (ii) Calculate the electrostatic potential energy of the D–T system at this separation. (iii) Equate the result of part (ii) to the average thermal kinetic energy 32kT\tfrac32 kT of each nucleus and hence determine the minimum temperature (in kelvin) that the plasma must reach for fusion to become energetically possible.

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