# Problem set 4

# Mass, Binding Energy and the Liquid Drop Model

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**1:**

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

- 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

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

- Calculate the mass of the following nuclides: n,
^{1}H,^{56}Fe,^{142}Ce and^{238}U - Which of these nuclides are the most stable?
- Assume that 1.00 kg
^{2}H fuse to give pure^{4}He. What is the change in mass and what is the amount of energy produced (Mev and kWh)? - Assume 1.00 kg
^{233}U fission spontaneously and that the products are only^{92}Rb,^{128}Cs and 3 neutrons per fission. What is the change in mass and what is the energy produced? - Which form of energy associated with fission is the most important? Describe whether or not it is 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 sodium is 5.14 V?

**4:**

Use Einsteins formula to calculate the mass in kg of the following particles (n = ^{}939,6 MeV, e = 0.511 MeV, u = 931.5):

- A neutron.
- An 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 a ^{233}U nucleon fissions into a ^{131}Xe nucleus, a ^{101}Ru nucleus and 3 neutrons. What are their respective energies?

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

**7:**

Assume 200 MeV releases per nucleus when uranium fissions . How far can you drive a car with 1 g of ^{235}U as fuel when a car uses approximately 1 L of gasoline (density 0.70 g/cm^{3}) 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.

**8:**

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).

ΔG for H_{2}O is -237 kJ/mol and 0.0303 u is liberated when two protons two neutrons and two electrons 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 isobar chains with odd number of nucleons, while isobar chains with even number of nucleons can have more than one.

**11:**

Explain where we find nuclides with both β^{+} and β^{-} disintegration. Why do these nuclides have odd number of protons and odd number of neutrons?