Find the total binding energy for Germanium, 72Ge (atomic mass = 71.922079 u). M

Question

Find the total binding energy for Germanium, 72Ge (atomic mass = 71.922079 u). MeV

2. Calculate the average binding energy per nucleon for Thorium, 228Th (atomic mass = 228.028715 u). MeV

3. A drug prepared for a patient is tagged with 4399Tc which has a half life of 6.05 h and an activity of 1.90 µCi when it was prepared. Suppose the drug containing 4399Tc is injected into the patient 1.35 h after it is prepared. What is its activity at the time it is injected? µCi

4. An ancient club is found that contains 170 g of pure carbon and has an activity of 7.5 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.30 × 10-12. Note that the half life of carbon-14 is 5700 years and the Avogadro number is 6.02 × 1023. years

5. One of the many isotopes used in cancer treatment is 79198Au, with a half-life of 2.70 d. Determine the mass of this isotope that is required to give an activity of 260 Ci. mg

6. Suppose that the average power consumption per year in a typical house is 345 W. What initial mass of 92235U would have to undergo fission to supply the electrical needs of such a house for a year? (Assume 200 MeV is released per fission. The Avogadro number is 6.02 × 1023) g

7. What is the energy released in the fission reaction 01n + 92235U 57143La + 3590Br + 3 01n? (The atomic mass of 143La is 142.916063 u and that of 90Br is 89.930638 u) MeV

8. What is the energy released in this nuclear reaction 88230Ra 89230Ac + -10e? (The atomic mass of 230Ra is 230.037056 u and that of 230Ac is 230.036293 u) MeV

9. What is the energy released in this nuclear reaction 49Be + 11H 36Li + 24He? (The atomic mass of 9Be is 9.012182 u, and that of 6Li is 6.015121 u) MeV

10. A neutron causes 90232Th to change according to the following reaction: 01n + 90232Th ZAX + The ZAX nucleus subsequently undergoes - decay, and its daughter does too. What is the atomic number of the final nucleus?

Explanation / Answer

mass of neutron = Mn = 1.00898 u

mass of proton = Mp = 1.00759 u

Z = atomic number ( number of protons)

A = mass number

A-Z = number of neutrons

total mass of the nucleus M' = (Z*Mp) + (A-z)*Mn

M' = (32*1.00759) + ((72-32)*1.00898) = 72.60208 u

Mass defect dM = M' - M = 72.60208 - 71.922079 = 0.680001 u

energy of 1 u = 931.5 Mev

binding energy BE = dM*931.5 Mev

BE = 0.680001*931.5 = 633.4209315 MeV

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(2)

mass of neutron = Mn = 1.00898 u

mass of proton = Mp = 1.00759 u

Z = atomic number ( number of protons)

A = mass number

A-Z = number of neutrons

total mass of the nucleus M' = (Z*Mp) + (A-z)*Mn

M' = (90*1.00759) + ((228-90)*1.00898) = 229.92234 u

Mass defect dM = M' - M = 229.92234 - 228.028715 = 1.893625 u

energy of 1 u = 931.5 Mev

binding energy BE = dM*931.5 Mev

BE = 1.893625*931.5 = 1763.9116875 MeV

average BE = BE/A = 1763.9116875/228 = 7.74 Mev/ nucleon

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6)

let m be the mass of U235 required

number of moles n = m/M

number of nuclei N = n*NA

NA = avagadro number

energy released E = N*200 MeV

1 MeV = 10^6*1.6*10^-19 J

energy required = P*t = 345*365*24*60*60 = 6307200000 J

therefore

m/M*NA*345*10^6*1.6*10^-19 = 6307200000

m/235*6.02*10^23*345*10^6*1.6*10^-19 = 6307200000

mass m = 44.6 grams <<<<,--------answer

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7)

mass of the reactants = 235.043930 + 1.00898 = 236.05291 u

mass of the products = 142.916063 + 89.930638 + (3*1.00898) = 235.873641 u

mass defect = mass of the reactants - mass of the products

mass defect dM = 236.05291 - 235.873641 = 0.179269 u

energy released E = dM*931.5 = 0.179269*931.5 = 166.9890735 MeV

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8)

mass of the reactants = 230.037056

mass of the products = 230.036293

mass defect = mass of the reactants - mass of the products

mass defect dM = 230.037056 - 230.036293 = 0.000763 u

energy released E = dM*931.5 = 0.000763*931.5 = 0.7107345 MeV

+++++++++++++++

9)

mass of the reactants = 9.012182 + (11*1.00759) = 20.095672 u

mass of the products = 6.015121 + 4.002602 = 10.017723

mass defect = mass of the reactants - mass of the products

mass defect dM = 20.095672 - 10.017723= 10.077949 u

energy released E = dM*931.5 = 10.077949*931.5 = 9387.6094935 MeV

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