Exercises+with+Mass,+Binding+Energy+and+the+Liquid+Drop+Model

  For this exercise the mass excess is used. The needed values are:
 * 1: **
 * n: 8.0713171 MeV.
 * 1 H: 7.28897050 MeV.
 * 4 He: 2.42491656 MeV.
 * 56 Fe: -60.6054 MeV.
 * 142 Ce: -84.583 MeV.
 * 238 U: 47.3089 MeV.


 * 1) Calculate the mass of the following nuclei: n, 1 H, 56 Fe, 142 Ce and 238 U
 * 2) Which of these nuclei are the most stable?
 * 3) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Assume that 1.00 kg 2 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">H fuse to give pure 4 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">He. What is the change in mass and what is the amount of energy produced (MeV and kWh)?
 * 4) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Assume 1.00 kg 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U fission spontaneously and that the products are only 92 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Rb, 128 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Cs and 3 neutrons per fission. What is the change in mass and what is the energy produced?
 * 5) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Which form of energy associated with fission is the most important? Describe whether or not it is radiation or some other form of energy.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">2: **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Calculate the binding energy per nucleon for 24 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Mg by using a table or database for atomic mass excess.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">3: **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">What is the ratio between the nuclear binding energy and the electron binding energy for 23 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Na when the ionization potential of sodium is 5.14 V?

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> **4:**

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Use Einstein’s formula to calculate the mass in kg of the following particles (n = 939.6 MeV, e = 0.511 MeV, u = 931.5 MeV):


 * 1) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">A neutron.
 * 2) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">An electron.
 * 3) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">The atomic mass unit “u”.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5: **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Calculate the average binding energy, given in MeV of the nucleons in the following nuclei:


 * 1) 40 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Ca with mass 29.9627 u.
 * 2) 56 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Fe with mass 55.9352 u.
 * 3) 208 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Pb with mass 207.9775 u.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">6: **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Assume a 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U nucleon fissions into a 131 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Xe nucleus, a 101 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Ru nucleus and 3 neutrons. What are their respective energies?


 * 235 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U: 40.916 MeV.
 * 131 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Xe: -88.421 MeV.
 * 101 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Ru: -87.952 MeV.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Neutron: 8.071 MeV.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">7: **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Assume 200 MeV releases per nucleus when uranium fissions. How far can you drive a car with 1 g of 235 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U as fuel when a car uses approximately 1 L of gasoline (density 0.70 g/cm 3 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">) for every 10 km? The heat of burning for octane is 5500 kJ/mole and a gasoline engine can utilize 18% of the total energy.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">8: **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Calculate the amount of energy released between a reaction of hydrogen and oxygen compared to the energy released with the creation of He from neutrons and hydrogen (proton + electron).

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> ΔG for H2O is -237 kJ/mol and 0.0303 u is liberated when two protons two neutrons and two electrons fuse to a He-atom.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> **9:**

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Determine if fusion of deuterium to helium gives more or less energy per gram than fission of uranium.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> **10:**

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Explain why we never find more than one stable nuclei in isobar chains with odd number of nucleons, while isobar chains with even number of nucleons can have more than one.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> **11:**

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Explain where we find nuclei with both β+ and β- disintegration. Why do these nuclei have odd number of protons and odd number of neutrons?

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