Question

3. A fission chain reaction. a. A neutron can cause 235U to fission, producing two daughter nuclei (tin and molybdenum) and three more neutrons. These three neutrons can then, in turn, cause three more 235U nuclei to split. One typical reaction is summarized as follows: n+25131Sn + 102Mo +3 n Find the energy released in this process (in MeV), given that MC3SU) 235.0439 u; M(3Sn) 130.9169 u; M(102Mo)-101.9103 u. b. Lise Meitner's work in 1938 predicted that the fission of 235U would produce 200 MeV of energy per fission event. How did she do? Find a 90-error. c. 131Sn is radioactive, and typical undergoes three successive B decays. What is the final product? d. How many nuclei are in 1 kg of 23sU? This is, incidentally, how many fission events occur if 1 kg of U were to fission.

Answer 1

(a) The energy released in the process can be calculated as follows: E Amc2 - [м(0) + м (п)-м("sn)-M ("-Мо)-зм(п)]e 102 235 131 931.5 MeV/c2 (235.0439 u -130.9169 u -101.9103 u-2(1.008664 u) 2 1u =185.72 MeV (b) The percentage error can be calculated as follows: 185.72-200 MeV (100)% %Error 185.72 = 7.69% (c) One decay increases the proton number by one. Thus, after 3 A decay the proton number increases by three. Hence, the atomic number of the resultant is, 50+3 = 53 Therefore, the final product is, 31 1. 53 (d) 235 235 g of uranium contains 6.022 x1025 nuclei. Hence, 1 kg of 6.022x 1025 (1000) nuclei 1 kg U contains, 235 g =2.56x1024 nuclei