Question

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1) Find the threshold energy for the following reaction:

2) Calculate the energy released in the fission reaction:

Answer 1

1)

2 6 0 8

Mass of Oxygen $M_O=15.99491\,amu$

Mass of neutron $M_n=1.008664\,amu$

Mass of carbon $M_C=13.00335\,amu$

Mass of Helium $M_{He}=4.00260\,amu$

Threshold energy $E_{th}=Q\frac{M_{products}+M_{reactants}}{2M_{target}}$

$Q=({M_{products}-M_{reactants}})c^2$

$E_{th}=\frac{(M_{products}-M_{reactants})(M_{products}+M_{reactants})}{2M_{target}}*931\,MeV$

$E_{th}=\frac{(M_C+M_{He}-M_n-M_O)(M_C+M_{He}+M_n+M_O)}{2M_{O}}*931\,MeV$

$E_{th}=2.352\,MeV$

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Mass of Helium $M_{He}=3.016029\,amu$

Mass of neutron $M_n=1.008664\,amu$

Mass of Hydrogen $M_{H}=2.014102\,amu$

$E_{th}=\frac{(M_{products}-M_{reactants})(M_{products}+M_{reactants})}{2M_{target}}*931\,MeV$

$E_{th}=\frac{(M_H+M_{H}-M_n-M_{He})(M_H+M_{H}+M_n+M_{He})}{2M_{He}}*931\,MeV$

$E_{th}=4.54\,MeV$

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2)

Energy released in fission process

136 54 235 38

Mass of Uranium $M_{U}=235.04393\,amu$

Mass of neutron $M_n=1.008664\,amu$

Mass of Strontium $M_{Sr}=87.905612\,amu$

Mass of Xenon $M_{Xe }=135.907219\,amu$

Mass of products $M_{products}=M_{Sr}+M_{Xe}+12M_n=235.9168\,amu$

Mass of reactants $M_{reactants}=M_U+M_{n}+12M_n=236.0526\,amu$

Energy released is $E=(M_{reactants}-M_{products})c^2=(236.0526-235.9168)*931=126.4\,MeV$