Question

The half life of Uranium-235 is 704 million years, yet it is unstable and naturally decays by alpha particle emission and can also undergo spontaneous fission. What is the binding energy per nucleon for the Uranium-235 and how does its binding energy per nucleon compare to that of the stable Carbon-12 nucleus that is ubiquitously present in biological systems? See the worked example for Carbon-12 shown in your lecture notes that is found throughout the human body as well as animal and plant kingdoms. Show your work!

Answer 1

p+ mass: 1.00729 amu n mass: 1.00867 amu

U235 has 92 protons and 143 neutrons.
atomic mass of U235: 235.0439299 amu

Δm = [92*1.00729 amu + 143 *1.00867 amu] -235.0439299 amu =1.8665601 amu
BE = ΔE = Δmc² = (1.8665601 amu * (1 g /6.022e23 amu) * (1 kg / 1000 g) ) * (3e8 m/s)²
BE = 2.78961157e-10 = 2.79 x 10^-10 J

BE per nucelon = 2.78961157e-10 / 235 = 1.18706875e-12 = 1.187 x10^-12 J/nucleon

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C-12
C has 6 neutrons and 6 protons.
Also, has atomic mass of 12 amu

Δm = [6*1.00729 + 6*1.00867] amu - 12 amu = 0.09576 amu

BE = 0.09576 amu *(1 g / 6.022e23 amu) * ( 1kg /1000g) * ( 3e8m/s)²
BE = 1.43115244e-11 J

BE/nucleon = 1.43115244e-11 / 12 nucleons = 1.19262703e-12 = 1.193x 10^-12 J/nucleon


BE/nucleon is higher for C-12