Semi-Empirical mass formula problem Problem 1 Semi-empirical mass formula is: A1

Question

Semi-Empirical mass formula problem

Problem 1 Semi-empirical mass formula is: A1/3 A1/2 where: av = 15.5 MeV as = 16.8 MeV ac = 0.7 MeV BA = 23 MeV aP = 34 MeV +1 0 -1 for even-even nuclei for even-odd nuclei for odd-odd nuclei = Use the semi-empirical mass formula to estimate the amount of prompt energy released when a 236U nucleus fissions into two equal fragments. This represents the prompt energy released by a fission event in a nuclear reactor. b . Our reactor on campus, when operatioal is 1 MW (w = joules/sec). Assming only the reaction above and 100% converse to heat, about how many fissions per second occour within the reactor when the reactor is operational? A gram of Uranium contains 2.5 x 1921 atoms. Assuming out 1 MW reactor is able to induce fission in 100% of the atoms, how, long (in units which match the time scale) would the reactor be able to run on 1 gram of fuel?

Explanation / Answer

a) 236U has Z=92 and A=236. Then the binding energy BEU = 1799.07 MeV.

The two equal fragments will be 118Pd. The BEPd = 990.71 MeV.

The energy released per nuclear fission E = 2* 990.71 - 1799.07 MeV = 182.35 MeV.

b) Power required 1MW = 10^6 J/s

Number of fissions reactions per second = 10^6 J/ 182.35 MeV = 3.43 x 10^16 fission reactions.

c) Run time for reacor with 1gm of 236U = (2.5 x 10^19) / (3.43 x 10^16) = 728.86 s.

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