(a)
Interpretation:
Binding energy per nucleon of 59Co has to be calculated in MeV.
Concept Introduction:
Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.
Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.
Nucleus + nuclear binding energy → nucleons
It can be calculated in MeV using the given formula,
Binding energy = Δm(in amu)×931.5 MeV1 amu
Nucleon: Nucleon is the collective name given to the members of the nucleus that is protons and neutrons.
The difference between mass of an atom and the sum of the masses of its proton and neutron is called Mass difference.
Binding Energy per Nucleon can be determined as follows:
Binding energy per nucleon = Binding energyNo. of nucleons
(a)
Explanation of Solution
Given information is shown below,
Mass of Cobalt-59 is 58.933198 amu.
In 59Co, there are 27 protons and 32 neutrons.
- Calculate the mass difference:
As known the mass H atom is 1.007825 amu and mass of neutron is 1.008665 amu.
Mass difference in 59Co can be calculated as given,
Δm = [(27×mass H atom)+(32×mass of neutron)]−[58.933198 amu]= [(27×1.007825 amu)+(32×1.008665 amu)]−[58.933198 amu]= [(27.211275 amu)+(32.27728 amu)]−[58.933198 amu]= 0.555357 amu
Mass difference in 59Co is 0.555357 amu.
- Calculate the binding energy per nucleon:
Number of nucleons in 59Co is 59.
Binding energy per nucleon of 59Co in MeV is calculated as follows,
Binding Energy per Nucleon= Δm(in amu)×931.5 MeV1 amuNo. of nucleons= (0.555357 amu)×931.5 MeV1 amu59 nucleons= 8.768 MeV/nucleon
Binding energy per nucleon of 59Co is 8.768MeV/nucleon.
(b)
Interpretation:
Binding energy per atom of 59Co has to be calculated in MeV.
Concept Introduction:
Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.
Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.
Nucleus + nuclear binding energy → nucleons
It can be calculated in MeV using the given formula,
Binding energy = Δm(in amu)×931.5 MeV1 amu
The difference between mass of an atom and the sum of the masses of its proton and neutron is called Mass difference.
(b)
Explanation of Solution
Given information is shown below,
Mass of Cobalt-59 is 58.933198 amu.
In 59Co, there are 27 protons and 32 neutrons.
- Calculate the mass difference:
As known the mass H atom is 1.007825 amu and mass of neutron is 1.008665 amu.
Mass difference in 59Co can be calculated as given,
Δm = [(27×mass H atom)+(32×mass of neutron)]−[58.933198 amu]= [(27×1.007825 amu)+(32×1.008665 amu)]−[58.933198 amu]= [(27.211275 amu)+(32.27728 amu)]−[58.933198 amu]= 0.555357 amu
Mass difference in 59Co is 0.555357 amu.
- Calculate the binding energy per atom:
Binding energy per atom of 59Co in MeV is calculated as follows,
Binding Energy per Atom= Δm(in amu)×931.5 MeV1 amuAtom= (0.555357 amu)×931.5 MeV1 amu1 atom= 517.3 MeV/atom
Binding energy per atom of 59Co is 517.3MeV/atom.
(c)
Interpretation:
Binding energy per mole of 59Co has to be calculated in kJ.
Concept Introduction:
Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.
Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.
Nucleus + nuclear binding energy → nucleons
Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is,
ΔE = Δmc2where,Δm = Mass Differencec= Speed of light
The difference between mass of an atom and the sum of the masses of its proton and neutron is called Mass difference.
(c)
Explanation of Solution
Given information is shown below,
Mass of Cobalt-59 is 58.933198 amu.
In 59Co, there are 27 protons and 32 neutrons.
- Calculate the mass difference:
As known the mass H atom is 1.007825 amu and mass of neutron is 1.008665 amu.
Mass difference in 59Co can be calculated as given,
Δm = [(27×mass H atom)+(32×mass of neutron)]−[58.933198 amu]= [(27×1.007825 amu)+(32×1.008665 amu)]−[58.933198 amu]= [(27.211275 amu)+(32.27728 amu)]−[58.933198 amu]= 0.555357 amu = 0.555357 g/mol
Mass difference in 59Co is 0.555357 g/mol.
- Calculate the binding energy per mole:
Binding energy per mole of 59Co in kJ is calculated as follows,
Binding energy, E = Δmc2= (0.555357 g1 mol)(1 kg103 g)(2.998×108 m/s)2(1 J1 kg.m2.s−2)(1 kg103 J)= 4.99128×1010 kJ/mol
Binding energy per mole of 59Co is 4.99128×1010kJ/mol.
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Chapter 24 Solutions
Student Solutions Manual For Silberberg Chemistry: The Molecular Nature Of Matter And Change With Advanced Topics
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