Question #4 Calculate the binding energy (in MeV) and the binding energy per nuc
ID: 521229 • Letter: Q
Question
Question #4
Calculate the binding energy (in MeV) and the binding energy per nucleon of Potassium-39. [See appendix B for the relevant information]. For each type of decay state the resulting daughter nucleus: a) The proton emission of Bismuth-185 b) The beta decay of Calcium-51 c) The electron capture of Fermium-250 d) The alpha decay of Xenon-110 The activity of a sample of radioactive Silver-108 is 6.4 times 10^4 decays/s. Exactly 12 minutes later the activity of the sample is measured to be 2.0 times 10^3 decays/s. Use this information to calculate the half-life of Silver-108. The triple-alpha fusion process that occurs in the centers of some stars creates Carbon-12 nuclei by essentially fusing together three Helium-4 nuclei. Calculate the Q-value for this process in MeV. A beam of nuclei (with RBE = 16) is used for cancer therapy. Each nucleus in the beam has an energy of 125 MeV. The beam is focused on a 0.15 kg tumor which receives a biologically effective dose of 175 rem.Explanation / Answer
Answer (1)
Potassium is element # 19, so a neutral 39-K atom has 19 protons, 19 electrons, and 20 neutrons.
The binding energy of an atom is the difference between the sum of the rest masses of the constituent particles and the actual rest mass of the atom, multiplied by the speed of light in a vacuum squared. (Note that strictly speaking, the energy calculated in this way also includes the binding energy of the electrons, but this energy is negligibly small compared to the nuclear binding energy.)
The difference between the sum of the rest masses of the individual particles and the actual mass is called the "mass defect".
In this case,
mass defect = (19*1.007276 + 19*0.00054858 + 20*1.008665) AMU - 38.96371 AMU
mass defect = 0.358257 AMU
In kg, this is:
mass defect = 0.358257 AMU * 1.6605655*10^-27 kg/AMU
mass defect = 5.949092*10^-28 kg/atom
Binding energy = 5.949092*10^-28 kg/atom * c^2
Binding energy = 5.949092*10^-28 kg/atom * (2.997924*10^8 m/s)^2
Binding energy = 5.346776*10^-11 J/atom
= 333.7195 MeV/atom
To calculate the binding energy per mole, simply multiply by Avogadro's number:
Binding energy = 5.346776*10^-11 J/atom * 6.022*10^23 atoms/mol
Binding energy = 3.219828 * 10^13 J/mol