Concept explainers
(a)
Interpretation:
Binding energy per nucleon of 131I 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 Iodine-131 is 130.906114 amu.
In 131I, there are 53 protons and 73 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 131I can be calculated as given,
Δm = [(53×mass H atom)+(78×mass of neutron)]−[130.906114 amu]= [(53×1.007825 amu)+(78×1.008665 amu)]−[130.906114 amu]= [(53.414725 amu)+(78.675870 amu)]−[130.906114 amu]= 1.184481 amu
Mass difference in 131I is 1.184481 amu.
- Calculate the binding energy per nucleon:
Number of nucleons in 131I is 206.
Binding energy per nucleon of 131I in MeV is calculated as follows,
Binding Energy per Nucleon= Δm(in amu)×931.5 MeV1 amuNo. of nucleons= (1.184481 amu)×931.5 MeV1 amu206 nucleons= 8.422 MeV/nucleon
Binding energy per nucleon of 131I is 8.422MeV/nucleon.
(b)
Interpretation:
Binding energy per atom of 131I 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 Iodine-131 is 130.906114 amu.
In 131I, there are 53 protons and 73 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 131I can be calculated as given,
Δm = [(53×mass H atom)+(78×mass of neutron)]−[130.906114 amu]= [(53×1.007825 amu)+(78×1.008665 amu)]−[130.906114 amu]= [(53.414725 amu)+(78.675870 amu)]−[130.906114 amu]= 1.184481 amu
Mass difference in 131I is 1.184481 amu.
- Calculate the binding energy per atom:
Binding energy per atom of 131I in MeV is calculated as follows,
Binding Energy per Atom= Δm(in amu)×931.5 MeV1 amuAtom= (1.184481 amu)×931.5 MeV1 amu1 atom= 1103 MeV/atom
Binding energy per atom of 131I is 1103MeV/atom.
(c)
Interpretation:
Binding energy per mole of 131I 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 Iodine-131 is 130.906114 amu.
In 131I, there are 53 protons and 73 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 131I can be calculated as given,
Δm = [(53×mass H atom)+(78×mass of neutron)]−[130.906114 amu]= [(53×1.007825 amu)+(78×1.008665 amu)]−[130.906114 amu]= [(53.414725 amu)+(78.675870 amu)]−[130.906114 amu]= 1.184481 g/mol
Mass difference in 131I is 1.184481 g/mol.
- Calculate the binding energy per mole:
Binding energy per mole of 131I in kJ is calculated as follows,
Binding energy, E = Δmc2= (1.184481 g1 mol)(1 kg103 g)(2.998×108 m/s)2(1 J1 kg.m2.s−2)(1 kg103 J)= 1.06456×1011 kJ/mol
Binding energy per mole of 131I is 1.06456×1011kJ/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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