Problem#1
The most common isotope of boron is 11B5. (a) Determine the total binding energy of 11B5 . (b) Calculate this binding energy. (Why is the fifth term zero?) Compare to the result you obtained in part (a). What is the percent difference? Compare the accuracy for 11B5 to its accuracy for 62B28.Answer:
(a) A 11B5 atom has 5 protons, 11 – 5 = 6 neutrons, and 5 electrons. The mass defect therefore is
∆m = 5mp + 6mn + 5me – M(11B5)
∆m = 5(1.0072765 u) + 6(1.0086649 u) + 5(0.0005485799 u) – 11.009305 u = 0.08181 u
The energy equivalent is
EB = ∆Mc2 = 0.08181 uc2 = 0.08181u x 931.5 MeV/u = 76.21 MeV
(b) we use
EB = C1A – C2A2/3 – C3Z(Z – 1)/A1/3 – C4(A – 2Z)2/A
The fifth term is zero since Z is odd but N is even. 11 and 5.
EB = (15.75 MeV)(11) – (17.80 MeV)(11)2/3 – (0.7100 MeV)5(4)/111/3 – (23.69 MeV)(11 – 10)2/11
EB = +173.25 MeV – 88.04 MeV – 6.38 MeV – 2.15 MeV = 76.68 MeV
The percentage difference between the calculated and measured EB is
(76.68 MeV – 76.21 MeV)/76.21 MeV = 0.6%
Problem#2
The most common isotope of uranium, 238U92 has atomic mass 238.050783u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.
Answer:
The mass defect is the total mass of the constituents minus the mass of the atom.
1 u is equivalent to 931.5 MeV. 238 92U has 92 protons, 146 neutrons and 238 nucleons.
(a) the mass defect is
∆m = 146mn + 92mH – mU = 1.93u
(b) the binding energy is
∆E = ∆mc2 = 1.93uc2 = 1.93u x (931.5 MeV/u) = 1,798 MeV = 1.8 GeV
(c) the binding energy per nucleon is
∆E/nucleon = 1.8 GeV/238 nucleon = 7.56 MeV per nucleon
Problem#3
What is the maximum wavelength of a γ ray that could break a deuteron into a proton and a neutron? (This process is called photodisintegration.)
Answer:
The text calculates that the binding energy of the deuteron is 2.224 MeV. A photon that breaks the deuteron up into a proton and a neutron must have at least this much energy.
E = hc/λ
λ = hc/E = (6.62 x 10-34 Js)(2.998 x 108 m/s)/(2.224 x 106 eV x 1,602 x 10-19 J/eV)
λ = 5.575 x 10-13 m = 0.5575 pm
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