2. Nuclear binding energy a) Use the semi empirical mass formula to determine the mass of 16Er . How well does it agree
Posted: Tue May 17, 2022 8:46 pm
I need the solution of these Numericals of Nuclear Physics urgently.
2. Nuclear binding energy a) Use the semi empirical mass formula to determine the mass of 16Er . How well does it agree with the measured value? (see appendix C in the textbook by Krane). b) Estimate the energy needed to remove one neutron from "Ca nucleus (which has N=Z=20) c) The masses of the mirror nuclei ??Al and ??Si are 26.9981539 u and 26.986704 u, respectively. Use this to determine an approximate value of the Coulomb's coefficient in the semi-empirical mass formula. d) For A=135 find the most stable nucleus using the semi empirical mass formula. Sketch the mass as a function of Z for the A=135 isobars (“mass parabola") and explain how the beta decay flows between nuclei with A=135. Make also a sketch for a case where A is an even number, for example A=128, explain the difference from the odd A case. e) The following figure shows the binding energy per nucleon. - For which mass number A (approx.) do we find the most stable nucleus? - We can "fuse” two nuclei to one (fusion) or split a nucleus (fission). For which nuclei (approx ranges of A) can energy be produced through fusion or fission? - Can you explain the peaks observed for A<20 in the curve? Which nuclear model can explain these? For light nuclei the most stable nuclei have equal number of protons and neutrons, due to which term in the binding energy formula? As A increases which term becomes more important, leading to the stable nuclei having more neutrons than protons? And why? Binding Energy/A (MeV per nucleon) 10 20 40 80 120 160 200 240 Mass Number, A
2. Nuclear binding energy a) Use the semi empirical mass formula to determine the mass of 16Er . How well does it agree with the measured value? (see appendix C in the textbook by Krane). b) Estimate the energy needed to remove one neutron from "Ca nucleus (which has N=Z=20) c) The masses of the mirror nuclei ??Al and ??Si are 26.9981539 u and 26.986704 u, respectively. Use this to determine an approximate value of the Coulomb's coefficient in the semi-empirical mass formula. d) For A=135 find the most stable nucleus using the semi empirical mass formula. Sketch the mass as a function of Z for the A=135 isobars (“mass parabola") and explain how the beta decay flows between nuclei with A=135. Make also a sketch for a case where A is an even number, for example A=128, explain the difference from the odd A case. e) The following figure shows the binding energy per nucleon. - For which mass number A (approx.) do we find the most stable nucleus? - We can "fuse” two nuclei to one (fusion) or split a nucleus (fission). For which nuclei (approx ranges of A) can energy be produced through fusion or fission? - Can you explain the peaks observed for A<20 in the curve? Which nuclear model can explain these? For light nuclei the most stable nuclei have equal number of protons and neutrons, due to which term in the binding energy formula? As A increases which term becomes more important, leading to the stable nuclei having more neutrons than protons? And why? Binding Energy/A (MeV per nucleon) 10 20 40 80 120 160 200 240 Mass Number, A