Using the semi-emprical mass formula, show that the energy released when a nucleus (Z,A) emits an a-particle is given by Qa = -4ay + 8A/3 + 4acZ@-2/3A) – 4a,N-2 + B(2, 4), 4a A + B(2,4), where B(2,4) is the binding energy of the a-particle, 28.30 MeV.
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- What minimum energy E(min) is needed to remove a neutron from K40 and so convert it to K39? The atomic masses of the two isotopes are 39.964000 and 38.963708 u, respectively. E(min) = ? eVCalculate the energy released in the reaction, in MeV: 6Li + n = 4He + 3H mLi = 6.015123 u; mn = 1.008665 u; mHe = 4.002603 u; mH = 3.016049 u %3D %3DFind the binding energy per nucleon in J and eV for the three following isotopes, given their atomic masses in u: 33 Si silicon 32.97800017 u ☐ × 10-12 J ☐ MeV 241 Es einsteinium 241.0685424 u 99 ×10−12 J☐MeV 170 oxygen 16.9991317012 u ×10-¹² J MeV mhydrogen = 1.007825 u mneutron 1.008664915 u -27 u = 1.6605 × 101 kg
- The stable nuclei 36Ar and 76Se both differ by 20 in atomic number from 56Fe, which lies at the peak of the binding energy per nucleon curve. Find B/A for both 36Ar and 76Se. Which one has the larger B/A? Why is this to be expected?An unknown element X has the following isotopes: ⁶⁴X (49.00% abundant), ⁶⁶X (28.00% abundant), ⁶⁸X (23.00% abundant). What is the average atomic mass in amu of X?An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14C. Find the minimum age (in years) of the charcoal. Carbon-14 has a half-life of 5730 years which means half of it will be gone after 5730 years. You may find the equality 210 = 1024 to be useful.
- The mass of the atom 9F is 18.99840 amu. Calculate the binding energy per atom. Answer Units: [x10-11 J]2H is a loosely bound isotope of hydrogen, called deuterium or heavy hydrogen. It is stable but relatively rare — it form only 0.015% of natural hydrogen. Note that deuterium has Z = N, which should tend to make it more tightly bound, but both are odd numbers. Calculate BE/A, the binding energy per nucleon, for 2H in megaelecton volts per nucleon.Technetium has not been found in nature. It can be obtained readily as a product of uranium fission in nuclear power plants, however, and is now produced in quantities of many kilograms per year. One medical use relies on the tendency of 99mTc (an excited nuclear state of 99Tc) to concentrate in abnormal heart tissue. Calculate the total activity (in disintegrations per second) caused by the decay of 1.0 mg of 99mTc, which has a half-life of 6.0 hours.
- ts) We can approximate the 232Th nucleus as a one-dimensional infinite square well with length L equal to the nuclear radius R = R₁A¹/3, where Ro = 1.2 fm and A is the atomic mass number. (a) What is the length of this infinite square well? What is the ground state energy of a proton (which has mass m₂ = 938.3 MeV/c²) in this infinite square well? (b) 232Th has 90 protons and 142 neutrons. Assume that all these protons and neutrons trapped in the infinite square well. How many energy levels of this infinite square well contain protons? How many energy levels contain neutrons?When a nucleus decays, the daughter nucleus can be in an excited state. The 93/43Tc nucleus (molar mass 92.910 2 g/mol) in the ground state decays by electron capture and e+ emission to energy levels of the daughter (molar mass 92.906 8 g/mol in the ground state) at 2.44 MeV, 2.03 MeV, 1.48 MeV, and 1.35 MeV. (a) Identify the daughter nuclide. (b) To which of the listed levels of the daughter are electron capture and e+ decay of 93/43Tc allowed?