Consider the decay of 235U → 231Th → 231Pa, with a half-life of 7.038x108 years for 235U and 25.5 hours for 231Th. Suppose you have a sample with 10 mCi of 235U. Calculate and plot the activities of the father and daughter as a function of time (assume the granddaughter is stable) between t = 0 and 1000 hours. If you find it convenient, use a logarithmic scale. What kind of balance is there and why? In the graph, indicate the time tm (remember tm = [1/( λ2 - λ1)] [ln(λ2 / λ1]) in which the daughter reaches her maximum activity and verify that it coincides with the analytical expression calculated in class.

The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars. These stars eventually explode, releasing the elements into space. If we assume that at the time of explosion there were equal amounts of 235U and 238U, 235 how long ago were the elements that formed our Earth released, given that the present U/238U ratio is 0.007? (The half-lives of 235u and 238U are 0.70 × 10° yr and 4.47 x 10° yr, respectively.) years

We want to get an idea of the actual mass of 235U involved in powering a nuclear power plant. Assume that a single fission event releases 200 MeV of thermal energy. A 1,000 MWe electric power plant has a thermal power of approximately 3,000 MWth. What rate of fission reactions is required to produce this power? (Note: 1 eV = 1.6 × 10−19 J.) The reactor core consists of approximately 100 tonnes of UO2 (1 tonne = 1,000 kg), which is enriched in 235U to 4%. How many full-power years could the reactor operate if all of the 235U were to be fissioned? What factors prevent such complete depletion of the 235U from occurring? Under the 235U depletion scenario of part b, what mass of fission products and what mass of high-level wastes (HLW) would be produced?

Calculate the energy released in the following fission reaction: 232Tn + n → 99Kr +124Xe + 10n  (Express your answer to five significant figures in MeV) Recall that the atomic masses are 232Th = 232.038051 u, 99Kr = 98.957606 u, and 124Xe = 123.905894 u.

In nuclear reaction: [ 220Rn ? 216Po + α ] a Radon-220 atom undergoes alpha decay. The components have these atomic mass energies: 220Rn : 204941 MeV, 216Po : 201206 MeV, α : 3727 MeV. About how much energy is released in this reaction?