MCGRAW: CHEMISTRY THE MOLECULAR NATURE
MCGRAW: CHEMISTRY THE MOLECULAR NATURE
8th Edition
ISBN: 9781264330430
Author: VALUE EDITION
Publisher: MCG
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Chapter 24, Problem 24.80P

(a)

Interpretation Introduction

Interpretation:

Binding energy per nucleon of 206Pb 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)

Expert Solution
Check Mark

Explanation of Solution

Given information is shown below,

Mass of Lead-206 is 205.974440 amu.

In 206Pb, there are 82 protons and 124 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 206Pb can be calculated as given,

  Δm = [(82×mass H atom)+(124×mass of neutron)][205.974440 amu]= [(82×1.007825 amu)+(124×1.008665 amu)][205.974440 amu]= [(82.641650 amu)+(125.074460 amu)][205.974440 amu]= 1.741670 amu

Mass difference in 206Pb is 1.741670 amu.

  • Calculate the binding energy per nucleon:

Number of nucleons in 206Pb is 206.

Binding energy per nucleon of 206Pb in MeV is calculated as follows,

  Binding Energy per Nucleon= Δm(in amu)×931.5 MeV1 amuNo. of nucleons= (1.741670 amu)×931.5 MeV1 amu206 nucleons= 7.876 MeV/nucleon

Binding energy per nucleon of 206Pb is 7.876 MeV/nucleon.

(b)

Interpretation Introduction

Interpretation:

Binding energy per atom of 206Pb 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)

Expert Solution
Check Mark

Explanation of Solution

Given information is shown below,

Mass of Lead-206 is 205.974440 amu.

In 206Pb, there are 82 protons and 124 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 206Pb can be calculated as given,

  Δm = [(82×mass H atom)+(124×mass of neutron)][205.974440 amu]= [(82×1.007825 amu)+(124×1.008665 amu)][205.974440 amu]= [(82.641650 amu)+(125.074460 amu)][205.974440 amu]= 1.741670 amu

Mass difference in 206Pb is 1.741670 amu.

  • Calculate the binding energy per atom:

Binding energy per atom of 206Pb in MeV is calculated as follows,

  Binding Energy per Atom= Δm(in amu)×931.5 MeV1 amuAtom= (1.741670 amu)×931.5 MeV1 amu1 atom= 1622 MeV/atom

Binding energy per atom of 206Pb is 1622 MeV/atom.

(c)

Interpretation Introduction

Interpretation:

Binding energy per mole of 206Pb 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)

Expert Solution
Check Mark

Explanation of Solution

Given information is shown below,

Mass of Lead-206 is 205.974440 amu.

In 206Pb, there are 82 protons and 124 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 206Pb can be calculated as given,

  Δm = [(82×mass H atom)+(124×mass of neutron)][205.974440 amu]= [(82×1.007825 amu)+(124×1.008665 amu)][205.974440 amu]= [(82.641650 amu)+(125.074460 amu)][205.974440 amu]= 1.741670 amu = 1.741670 g/mol

Mass difference in 206Pb is 1.741670 g/mol.

  • Calculate the binding energy per mole:

Binding energy per mole of 206Pb in kJ is calculated as follows,

Binding energy, E = Δmc2= (1.741670 g1 mol)(1 kg103 g)(2.998×108 m/s)2(1 J1 kg.m2.s2)(1 kg103 J)= 1.56533×1011 kJ/mol

Binding energy per mole of 206Pb is 1.56533×1011 kJ/mol.

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Chapter 24 Solutions

MCGRAW: CHEMISTRY THE MOLECULAR NATURE

Ch. 24.2 - Prob. 24.6AFPCh. 24.2 - Prob. 24.6BFPCh. 24.6 - Prob. 24.7AFPCh. 24.6 - Prob. 24.7BFPCh. 24.7 - Prob. B24.1PCh. 24.7 - Prob. B24.2PCh. 24.7 - Prob. B24.3PCh. 24.7 - Prob. B24.4PCh. 24 - Prob. 24.1PCh. 24 - Prob. 24.2PCh. 24 - Prob. 24.3PCh. 24 - Prob. 24.4PCh. 24 - Prob. 24.5PCh. 24 - Prob. 24.6PCh. 24 - Prob. 24.7PCh. 24 - Prob. 24.8PCh. 24 - Prob. 24.9PCh. 24 - Prob. 24.10PCh. 24 - Prob. 24.11PCh. 24 - Prob. 24.12PCh. 24 - Prob. 24.13PCh. 24 - Prob. 24.14PCh. 24 - Prob. 24.15PCh. 24 - Prob. 24.16PCh. 24 - Prob. 24.17PCh. 24 - Prob. 24.18PCh. 24 - Prob. 24.19PCh. 24 - Prob. 24.20PCh. 24 - Prob. 24.21PCh. 24 - Prob. 24.22PCh. 24 - Prob. 24.23PCh. 24 - Prob. 24.24PCh. 24 - Prob. 24.25PCh. 24 - Prob. 24.26PCh. 24 - Prob. 24.27PCh. 24 - Prob. 24.28PCh. 24 - Prob. 24.29PCh. 24 - Prob. 24.30PCh. 24 - Prob. 24.31PCh. 24 - Prob. 24.32PCh. 24 - Prob. 24.33PCh. 24 - Prob. 24.34PCh. 24 - Prob. 24.35PCh. 24 - Prob. 24.36PCh. 24 - Prob. 24.37PCh. 24 - Prob. 24.38PCh. 24 - Prob. 24.39PCh. 24 - Prob. 24.40PCh. 24 - Prob. 24.41PCh. 24 - Prob. 24.42PCh. 24 - Prob. 24.43PCh. 24 - Prob. 24.44PCh. 24 - Prob. 24.45PCh. 24 - Prob. 24.46PCh. 24 - Prob. 24.47PCh. 24 - Prob. 24.48PCh. 24 - Prob. 24.49PCh. 24 - Prob. 24.50PCh. 24 - Prob. 24.51PCh. 24 - Prob. 24.52PCh. 24 - Prob. 24.53PCh. 24 - Prob. 24.54PCh. 24 - Prob. 24.55PCh. 24 - Prob. 24.56PCh. 24 - Prob. 24.57PCh. 24 - Prob. 24.58PCh. 24 - Prob. 24.59PCh. 24 - Prob. 24.60PCh. 24 - Prob. 24.61PCh. 24 - Prob. 24.62PCh. 24 - Prob. 24.63PCh. 24 - Prob. 24.64PCh. 24 - Prob. 24.65PCh. 24 - Prob. 24.66PCh. 24 - Prob. 24.67PCh. 24 - Prob. 24.68PCh. 24 - Prob. 24.69PCh. 24 - Prob. 24.70PCh. 24 - Prob. 24.71PCh. 24 - Prob. 24.72PCh. 24 - Prob. 24.73PCh. 24 - Prob. 24.74PCh. 24 - Prob. 24.75PCh. 24 - Prob. 24.76PCh. 24 - Prob. 24.77PCh. 24 - Prob. 24.78PCh. 24 - Prob. 24.79PCh. 24 - Prob. 24.80PCh. 24 - Prob. 24.81PCh. 24 - Prob. 24.82PCh. 24 - Prob. 24.83PCh. 24 - Prob. 24.84PCh. 24 - Prob. 24.85PCh. 24 - Prob. 24.86PCh. 24 - Prob. 24.87PCh. 24 - Prob. 24.88PCh. 24 - Prob. 24.89PCh. 24 - Prob. 24.90PCh. 24 - Prob. 24.91PCh. 24 - Prob. 24.92PCh. 24 - Prob. 24.93PCh. 24 - Prob. 24.94PCh. 24 - Prob. 24.95PCh. 24 - Prob. 24.96PCh. 24 - Prob. 24.97PCh. 24 - Prob. 24.98PCh. 24 - Prob. 24.99PCh. 24 - Prob. 24.100PCh. 24 - Prob. 24.101PCh. 24 - Prob. 24.102PCh. 24 - Prob. 24.103PCh. 24 - Prob. 24.104PCh. 24 - Prob. 24.105PCh. 24 - Prob. 24.106PCh. 24 - Prob. 24.107PCh. 24 - Prob. 24.108PCh. 24 - Prob. 24.109PCh. 24 - Prob. 24.110PCh. 24 - Prob. 24.111PCh. 24 - Prob. 24.112PCh. 24 - Prob. 24.113PCh. 24 - Prob. 24.114PCh. 24 - Prob. 24.115PCh. 24 - Prob. 24.116PCh. 24 - Prob. 24.117PCh. 24 - Prob. 24.118PCh. 24 - Prob. 24.119PCh. 24 - Prob. 24.120PCh. 24 - Prob. 24.121PCh. 24 - Prob. 24.122PCh. 24 - Prob. 24.123PCh. 24 - Prob. 24.124PCh. 24 - Prob. 24.125PCh. 24 - Prob. 24.126PCh. 24 - Prob. 24.127PCh. 24 - Prob. 24.128PCh. 24 - Prob. 24.129PCh. 24 - Prob. 24.130PCh. 24 - Prob. 24.131PCh. 24 - Prob. 24.132PCh. 24 - Prob. 24.133PCh. 24 - Prob. 24.134PCh. 24 - Prob. 24.135PCh. 24 - Prob. 24.136PCh. 24 - Prob. 24.137PCh. 24 - Prob. 24.138PCh. 24 - Prob. 24.139PCh. 24 - Prob. 24.140PCh. 24 - Prob. 24.141PCh. 24 - Prob. 24.142PCh. 24 - Prob. 24.143PCh. 24 - Prob. 24.144P
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