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, how long ago were the elements that formed our Earth released, given that the present 235U/238U ratio is 0.007? (The half-lives of 235U and 238U are 0.70 × 10º yr and 4.47 x 109 yr, respectively.) years

Consider the following decay: 232 U 92 a mass of 4.002603 u. 228 Th+ a. 232 U has a mass of 232.0371562 u, 228 Th has a mass of 228.0287411 u, and a has 90 92 90 A.) Determine the disintegration energy (Q-value) in MeV. Q= B.) Determine the KE of the daughter in MeV. KED= C.) Determine the KE of the a particle in MeV & as a factor of Q. KE= KE=Qx D.) Determine the speed of the particle in terms of c. For an a particle, E = 3.727 GeV. [NOTE: G stands for giga- which means 10º & M stands for mega- which means 106.] Vα = XC

Consider the following a-decay of the Uranium nucleus 236 U → 332Th + a. 90 (a) Show how the mass number (Aa) and atomic number (Za) of the alpha particle are obtained from this equation. (b) Calculate the Q-value (Qa) of the reaction. (c) Calculate the speed va = √2MQ of the alpha particle after it has been ejected from the parent nucleus, in terms of the speed of light c. M = -, mp and ma are the atomic masses (ma+mp) x ma mp of the daugher nucleus and the alpha particle, respectively. (d) Calculate the classical turning radius Re= 2Zpe²/Qa, where Zp is the atomic number of the daughter nucleus, and e² = 1.44 MeV. fm. (e) Calculate the decay probability Pa that the alpha particle will tunnel through the barrier. HINT: In calculating the probability, use the fact that ħc=197.327 MeV fm. The formula to use is given on page 5.

A sample of wood from an archaeological excavation is dated by using a mass spectrometer to measure the fraction of 14C atoms. Suppose 150 atoms of 14C are found for every 1.4×1015 atoms of 12C in the sample. What is the wood's age? Express your answer in years.