Question

2 Fission In symmetric fission, the nucleus of uranium238U) splits into two nuclei of palladium (11Pd). To a rough approximation, the nuclei of heavy atoms may be described as spheres with a uniform charge density of 1.33-1025 C/m3. (This is a reasonable approximation, so far as their electrical structure is concerned.) The charge of the uranium nucleus is +92e. Compute the initial electrostatic energy of the uranium nucleus and the electrostatic energy of the fission fragments once they have moved very far apart. You may ignore any interaction between the fission fragments (a) How much energy is released by a single uranium nucleus in this process? Give your result in both joules (J) and electron volts (ev). Pd Pd (b) How much energy would be released by symmetric fission of 1 g of 238U?

Answer 1

Total change an U = density into volume 92 times 1.6 times 10^-19 = 1.33 times 4/3 pi R^3 R = (2.64355 times 10^-33)^1/3 R = 2.979 times 10^-11 m Electrostatic energy of U = 3/5 k Q^2/R = 3/5 times 10^9 times (92 times 1.6 times 10^-19)^2/2.979 times^-11 = 3.9277 times 10^-14 J Electrostatic energy of Pd = 3/5 k Q prime^2/R prime R prime = R/(2)^1/3 = 2.3644 times 10^-11 m Energy of Pd = 3/5 times 9 times 190^9 times (46 times 1.6 times 10^-19)^2/2.3644 times 10^-11 = 1.2371 times 10^-14 J (a) Energy released fission = Electrostatic Energy of U - 2 times (that of Pd) = (3.9277 - 2 times 1.2371) times 10^-14 = 1.4535 times 10^-14 J = 9.072 times 10^4 eV (b) no. of U_nucleus in 1 g = 1/3.95 times 10^-22 = 2.53 times 10^21 Energy released by its fission = 1.4535 times 10^-14 times 2.53 times 10^21 J = 3.677 times 10^7 J or 2.295 times 10^26 eV