Napravio ovo gosn <b> §§N0§§ </b> <h1 class="text-center mb-4">Advanced Nuclear Physics Problems</h1> <div class="mb-4"> <h5>Solve the following problems:</h5> <div class="mb-3"> <p>(a) Calculate the energy released during the fusion of two deuterium nuclei: $$^2_1\text{H} + ^2_1\text{H} \rightarrow ^3_2\text{He} + n$$ Given the masses: $$m(^2_1\text{H}) = §§V0(2.013,2.015,0.0001)§§ \, \text{u}, \, m(^3_2\text{He}) = §§V1(3.014,3.016,0.0001)§§ \, \text{u}, \, m(n) = §§V2(1.008,1.009,0.0001)§§ \, \text{u}$$ Use \(1 \, \text{u} = 931.5 \, \text{MeV/c}^2\).</p> </div> <div class="mb-3"> <p>(b) The half-life of a radioactive isotope is §§V3(5,50,5)§§ years. Calculate the time required for its activity to decrease to §§V4(10,50,10)§§% of the initial activity. Use the decay law: $$A(t) = A_0 e^{-\lambda t}, \, \lambda = \frac{\ln(2)}{T_{1/2}}.$$</p> </div> <div class="mb-3"> <p>(c) A uranium-235 nucleus absorbs a neutron and undergoes fission: $$^{235}_{92}\text{U} + n \rightarrow ^{144}_{56}\text{Ba} + ^{89}_{36}\text{Kr} + 3n$$ Calculate the total energy released, given: $$m(^{235}_{92}\text{U}) = §§V5(235.04,235.06,0.0001)§§ \, \text{u}, \, m(n) = §§V6(1.008,1.009,0.0001)§§ \, \text{u},$$ $$m(^{144}_{56}\text{Ba}) = §§V7(143.92,143.95,0.0001)§§ \, \text{u}, \, m(^{89}_{36}\text{Kr}) = §§V8(88.92,88.95,0.0001)§§ \, \text{u}.$$</p> </div> <div class="mb-3"> <p>(d) Calculate the critical mass for a spherical uranium-235 assembly. Assume the average neutron mean free path is \(l = §§V9(2,5,0.1)§§ \, \text{cm}\), and the density of uranium-235 is \(\rho = §§V10(18,19,0.1)§§ \, \text{g/cm}^3\). Use the formula: $$M_c = \frac{4}{3} \pi R_c^3 \rho, \, R_c = 2l.$$</p> </div> <div class="mb-3"> <p>(e) A nuclear reactor produces §§V11(500,1500,100)§§ MW of thermal power. Calculate the mass of uranium-235 consumed per day if each fission releases \(E_f = 200 \, \text{MeV}\). Use: $$1 \, \text{MeV} = 1.602 \times 10^{-13} \, \text{J}, \, \text{Avogadro's number} = 6.022 \times 10^{23}.$$</p> </div> </div> <div class="text-center text-muted mt-5"> © 2025 Advanced Nuclear Physics. All Rights Reserved. </div>