Difference between revisions of "Problem set 4"

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= Masses and Binding Energy  =
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= Mass, Binding Energy and the Liquid Drop Model  =
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====== Return to [[Problem Solving Sets]] ======
  
 
<br>  
 
<br>  
  
<br>
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'''1:'''
  
'''1:''' For this exercise the mass excess is used. The needed values are:<br>  
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For this exercise the mass excess is used. The needed values are:<br>  
  
*n: 8071.3171 keV
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*n: 8.0713171 MeV
*<sup>1</sup>H: 7288.97050 keV
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*<sup>1</sup>H: 7.28897050 MeV
*<sup>4</sup>He: 2424.91656 keV
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*<sup>4</sup>He: 2.42491656 MeV
*<sup>56</sup>Fe: -60605.4 keV
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*<sup>56</sup>Fe: -60.6054 MeV
*<sup>142</sup>Ce: -84583 keV
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*<sup>142</sup>Ce: -84.583 MeV
*<sup>238</sup>U: 47308.9 keV
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*<sup>238</sup>U: 47.3089 MeV
  
 
more values can be found at [http://ie.lbl.gov/toi2003/MassSearch.asp http://ie.lbl.gov/toi2003/MassSearch.asp]  
 
more values can be found at [http://ie.lbl.gov/toi2003/MassSearch.asp http://ie.lbl.gov/toi2003/MassSearch.asp]  
  
#Calculate the mass of the following nucleides: n, <sup>1</sup>H, <sup>56</sup>Fe, <sup>142</sup>Ce and <sup>238</sup>U  
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#Calculate the mass of the following nuclides: n, <sup>1</sup>H, <sup>56</sup>Fe, <sup>142</sup>Ce and <sup>238</sup>U  
#Which of these nuclieds is the most stable.
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#Which of these nuclides are the most stable?
#Assume that 1.00 kg <sup>2</sup>H fuse to give pure <sup>4</sup>He. What is the change in mass, what is the amount of energy produced (Mev and kWh)  
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#Assume that 1.00 kg <sup>2</sup>H fuse to give pure <sup>4</sup>He. What is the change in mass and what is the amount of energy produced (Mev and kWh)?
#Assume 1.00 kg<sup>233</sup>U fission spontaniusly and that the products only are <sup>92</sup>Rb and <sup>128</sup>Cs and 3 netruons per fission. What is the change in mass and what is the energy produced  
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#Assume 1.00 kg <sup>233</sup>U fission spontaneously and that the products are only <sup>92</sup>Rb, <sup>128</sup>Cs and 3 neutrons 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?
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#Which form of energy associated with fission is the most important? Describe whether or not it is radiation or some other form of energy.
  
 
<br>  
 
<br>  
  
'''2:''' Calculate the binding energy per nucleon for 24 Mg by using a table or database for atomic mass excess.<br>  
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'''2:'''  
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Calculate the binding energy per nucleon for <sup>24</sup>Mg by using a table or database for atomic mass excess.<br>  
  
<br>'''3:''' What is the ratio between the nuclear binding energy and the electron binding energy for <sup>23</sup>Na when the ionisation potential of natrium is 5.14 V?<br>
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<br>'''3:'''  
  
<br>'''4:''' Use Einsteins formula and calculate the mass in MeV of the following particles:<br>  
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What is the ratio between the nuclear binding energy and the electron binding energy for <sup>23</sup>Na when the ionisation potential of sodium is 5.14 V?<br>
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<br>'''4:'''  
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Use Einsteins formula to calculate the mass in kg of the following particles (n = <sup></sup>939,6 MeV,&nbsp;&nbsp;&nbsp; e = 0.511 MeV, u = 931.5):<br>  
  
 
#A neutron.  
 
#A neutron.  
#A electron.  
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#An electron.  
 
#The atomic mass unit “u”.
 
#The atomic mass unit “u”.
  
 
<br>  
 
<br>  
  
'''5:''' Calculate the average binding energy, given in MeV of the nucleons in the following nuclei:<br>  
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'''5:'''  
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Calculate the average binding energy, given in MeV of the nucleons in the following nuclei:<br>  
  
 
#<sup>40</sup>Ca with mass 29.9627 u.  
 
#<sup>40</sup>Ca with mass 29.9627 u.  
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<br>  
 
<br>  
  
'''6:''' Assume that a <sup>233</sup>U nucleon fission and you get a <sup>131</sup>Xe nucleus and a <sup>101</sup>Ru nucleus and 3 netruons. What is the energy&nbsp;?<br>  
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'''6:'''  
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Assume a <sup>233</sup>U nucleon fissions into a <sup>131</sup>Xe nucleus, a <sup>101</sup>Ru nucleus and 3 neutrons. What are their respective energies?<br>  
  
*235U: 40.916 MeV.  
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*<sup>235</sup>U: 40.916 MeV.  
*131Xe: -88.421 MeV.  
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*<sup>131</sup>Xe: -88.421 MeV.  
*101Ru: -87.952 MeV.  
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*<sup>101</sup>Ru: -87.952 MeV.  
 
*neutron: 8.071 MeV.
 
*neutron: 8.071 MeV.
  
 
<br>  
 
<br>  
  
'''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 <sup>235</sup>U as fuel. When a car uses aproximatly, unless american, 1L of gasoline (density 0.70 g/cm^3) for every 10 km? The heat of burning for catan is 5500kj/mole and a gasoline engine can use 18% of the energy.
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'''7:'''  
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Assume 200 MeV releases per nucleus when uranium fissions . How far can you drive a car with 1 g of <sup>235</sup>U as fuel when a car uses approximately 1 L of gasoline (density 0.70 g/cm<sup>3</sup>) 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.
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<br>'''8:'''
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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).
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<br><span class="texhtml"><span class="texhtml">Δ</span></span>G for H<sub>2</sub>O is -237 kJ/mol and 0.0303 u is liberated when two protons two neutrons and two electrons fuse to a He-atom.
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<br>'''9:'''
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Determine if fusion of deuterium to helium gives more or less energy per gram than fission of uranium.  
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<br>'''10:'''
  
<br>'''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).<br>DeltaG for H_2O is -237 kJ/mol and 0.0303 u is liberated when two protons two neutrons and two electronse fuse to a He-atom.
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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. <br>  
  
<br>'''9:''' Determine if fusion of deuterium to helium gives more or less energy per gram than fission of uranium.
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<br>'''11:'''  
  
<br>'''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.
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Explain where we find nuclides with both β<sup>+</sup> and β<sup>-</sup> disintegration. Why do these nuclides have odd number of protons and odd number of neutrons?<br><br><br>
  
<br>'''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.<br><br>
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[[Category:Unsolved_Problems]] [[Category:Bachelor]]

Latest revision as of 10:02, 9 July 2012

Mass, Binding Energy and the Liquid Drop Model

Return to Problem Solving Sets


1:

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

  • n: 8.0713171 MeV
  • 1H: 7.28897050 MeV
  • 4He: 2.42491656 MeV
  • 56Fe: -60.6054 MeV
  • 142Ce: -84.583 MeV
  • 238U: 47.3089 MeV

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

  1. Calculate the mass of the following nuclides: n, 1H, 56Fe, 142Ce and 238U
  2. Which of these nuclides are the most stable?
  3. Assume that 1.00 kg 2H fuse to give pure 4He. What is the change in mass and what is the amount of energy produced (Mev and kWh)?
  4. Assume 1.00 kg 233U fission spontaneously and that the products are only 92Rb, 128Cs and 3 neutrons per fission. What is the change in mass and what is the energy produced?
  5. 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 24Mg 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 23Na 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):

  1. A neutron.
  2. An electron.
  3. The atomic mass unit “u”.


5:

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

  1. 40Ca with mass 29.9627 u.
  2. 56Fe with mass 55.9352 u.
  3. 208Pb with mass 207.9775 u.


6:

Assume a 233U nucleon fissions into a 131Xe nucleus, a 101Ru nucleus and 3 neutrons. What are their respective energies?

  • 235U: 40.916 MeV.
  • 131Xe: -88.421 MeV.
  • 101Ru: -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 235U as fuel when a car uses approximately 1 L of gasoline (density 0.70 g/cm3) 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 H2O 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?