# Problem set 4

# Masses and Binding Energy

**1:** For this exercise the mass excess is used. The needed values are:

- n: 8071.3171 keV
^{1}H: 7288.97050 keV^{4}He: 2424.91656 keV^{56}Fe: -60605.4 keV^{142}Ce: -84583 keV^{238}U: 47308.9 keV

more values can be found at http://ie.lbl.gov/toi2003/MassSearch.asp

- Calculate the mass of the following nucleides: n,
^{1}H,^{56}Fe,^{142}Ce and^{238}U - Which of these nuclieds is the most stable.
- Assume that 1.00 kg
^{2}H fuse to give pure^{4}He. What is the change in mass, what is the amount of energy produced (Mev and kWh) - Assume 1.00 kg
^{233}U fission spontaniusly and that the products only are^{92}Rb and^{128}Cs and 3 netruons per fission. What is the change in mass and what is the energy produced - Which form of energy is the most importan with fission? Is it radiation or some other form of energy?

**2:** Calculate the binding energy per nucleon for ^{24}Mg by using a table or database for atomic mass excess.

**3:** What is the ratio between the nuclear binding energy and the electron binding energy for ^{23}Na when the ionisation potential of natrium is 5.14 V?

**4:** Use Einsteins formula and calculate the mass in MeV of the following particles:

- A neutron.
- A electron.
- The atomic mass unit “u”.

**5:** Calculate the average binding energy, given in MeV of the nucleons in the following nuclei:

^{40}Ca with mass 29.9627 u.^{56}Fe with mass 55.9352 u.^{208}Pb with mass 207.9775 u.

**6:** Assume that a ^{233}U nucleon fission and you get a ^{131}Xe nucleus and a ^{101}Ru nucleus and 3 netruons. What is the energy ?

^{235}U: 40.916 MeV.^{131}Xe: -88.421 MeV.^{101}Ru: -87.952 MeV.- neutron: 8.071 MeV.

**7:** Assume that by fission of uranium we get a energy of 200 MeV per nucleus. How far can you drive a car with 1 g of ^{235}U as fuel. When a car uses aproximatly 1L of gasoline (density 0.70 g/cm^{3}) for every 10 km? The heat of burning for octane is 5500kj/mole and a gasoline engine can utilize 18% of the energy.

**8:** calculate the ammount of energy between a reaction of hydrogen and oxygen compare the energy with that of creation of He from neutrons and hydrogen (proton+electron).

G for H_{2}O is -237 kJ/mol and 0.0303 u is liberated when two protons two neutrons and two electronse fuse to a He-atom.

**9:** Determine if fusion of deuterium to helium gives more or less energy per gram than fission of uranium.

**10:** explain why we never find more than one stable nuclide in a isobarchain of odd nummber but in a isobarchain of even number it is possible to find more.

**11:** explain where we can find nuclides that desintergates with both beta+ and beta-. In addition explain why they have to be nuclei with odd proton and odd neutron.