Chemistry: The Molecular Science
Chemistry: The Molecular Science
5th Edition
ISBN: 9781285199047
Author: John W. Moore, Conrad L. Stanitski
Publisher: Cengage Learning
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Chapter 18, Problem 23QRT
Interpretation Introduction

Interpretation:

Binding energy per nucleon for the two isotopes of boron has to be calculated and their stability has to be compared.

Concept Introduction:

Binding energy is a short strong force that is present in the nucleus which holds the protons together by overcoming the electrostatic repulsive forces between them.  Whenever there is a change in energy, a corresponding change in mass is also observed and this can be given by the equation shown below,

    ΔE = (Δm)c2

When more particles combine to form nuclear there is a great change in mass and energy.  The nuclear stabilities can be compared more appropriately by dividing the binding energy of nucleus with the number of nucleons.  The result obtained is the binding energy per nucleon.  Protons and neutrons are known as nucleons.  Binding energy is represented as Eb.

Expert Solution & Answer
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Explanation of Solution

Given equations in the problem statement is,

    5H11 + 5n01 B5105H11 + 6n01 B511

For B510:

The change in mass can be calculated as shown below,

Δm = (5×1.00783g/molH11)+(5×1.00867g/moln01)10.01294g/molB510 = 5.03915g/mol+5.04335g/mol10.01294g/mol = 10.0825g/mol10.01294g/mol = 0.06956g/mol

Nuclear binding energy can be calculated as shown below,

ΔE = (Δm)c2 = (0.06956g1mol×1kg1000g)×(2.99792×108m/s)2×1J1kgm2s-2×1kJ1000J = 0.6251×1010kJ/mol = 6.251×109kJ/mol

Binding energy per nucleon can be calculated as shown below,

There is a total of ten nucleons in boron-10.  Hence, the binding energy per nucleon can be calculated as,

    Eb = 6.251×109kJ10molnucleons = 6.251×108kJ/mol

Binding energy per nucleon in B510 is 6.251×108kJ/mol.

For B511:

The change in mass can be calculated as shown below,

Δm = (5×1.00783g/molH11)+(6×1.00867g/moln01)11.00931g/molB511 = 5.03915g/mol+6.05202g/mol11.00931g/mol = 11.09117g/mol11.00931g/mol = 0.08186g/mol

Nuclear binding energy can be calculated as shown below,

ΔE = (Δm)c2 = (0.08186g1mol×1kg1000g)×(2.99792×108m/s)2×1J1kgm2s-2×1kJ1000J = 0.7357×1010kJ/mol = 7.357×109kJ/mol

Binding energy per nucleon can be calculated as shown below,

There is a total of eleven nucleons in boron-11.  Hence, the binding energy per nucleon can be calculated as,

    Eb = 7.357×109kJ11molnucleons = 6.688×108kJ/mol

Binding energy per nucleon in B511 is 6.688×108kJ/mol.

On comparing the binding energy per nucleon for B510 and B511, it is found that B511 has more binding energy per nucleon than B510.  Hence, B511 is more stable than B510.

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Chapter 18 Solutions

Chemistry: The Molecular Science

Ch. 18.4 - Prob. 18.6PSPCh. 18.4 - Prob. 18.7PSPCh. 18.4 - Prob. 18.6ECh. 18.4 - Prob. 18.7CECh. 18.5 - Prob. 18.8ECh. 18.5 - Prob. 18.9CECh. 18.6 - Prob. 18.10ECh. 18.6 - Prob. 18.11ECh. 18.7 - Prob. 18.12ECh. 18.8 - Prob. 18.13ECh. 18.8 - Prob. 18.14ECh. 18.9 - Prob. 18.15ECh. 18 - Prob. 1SPCh. 18 - Prob. 2SPCh. 18 - Prob. 3SPCh. 18 - Prob. 4SPCh. 18 - Prob. 5SPCh. 18 - Prob. 1QRTCh. 18 - Prob. 2QRTCh. 18 - Prob. 3QRTCh. 18 - Prob. 4QRTCh. 18 - Prob. 5QRTCh. 18 - Prob. 6QRTCh. 18 - Prob. 7QRTCh. 18 - Prob. 8QRTCh. 18 - Prob. 9QRTCh. 18 - Complete the table.Ch. 18 - Prob. 11QRTCh. 18 - Prob. 12QRTCh. 18 - Prob. 13QRTCh. 18 - Prob. 14QRTCh. 18 - Prob. 15QRTCh. 18 - Prob. 16QRTCh. 18 - Prob. 17QRTCh. 18 - Prob. 18QRTCh. 18 - Prob. 19QRTCh. 18 - Prob. 20QRTCh. 18 - Prob. 21QRTCh. 18 - Prob. 22QRTCh. 18 - Prob. 23QRTCh. 18 - Prob. 24QRTCh. 18 - Prob. 25QRTCh. 18 - Prob. 26QRTCh. 18 - Prob. 27QRTCh. 18 - Prob. 28QRTCh. 18 - Prob. 29QRTCh. 18 - Prob. 30QRTCh. 18 - Prob. 31QRTCh. 18 - Prob. 32QRTCh. 18 - Prob. 33QRTCh. 18 - Prob. 34QRTCh. 18 - Prob. 35QRTCh. 18 - Prob. 36QRTCh. 18 - Prob. 37QRTCh. 18 - Prob. 38QRTCh. 18 - Prob. 39QRTCh. 18 - Prob. 40QRTCh. 18 - Prob. 41QRTCh. 18 - Prob. 42QRTCh. 18 - Prob. 43QRTCh. 18 - Prob. 44QRTCh. 18 - Prob. 45QRTCh. 18 - Prob. 46QRTCh. 18 - Prob. 47QRTCh. 18 - Prob. 48QRTCh. 18 - Prob. 49QRTCh. 18 - Prob. 50QRTCh. 18 - Prob. 51QRTCh. 18 - Prob. 52QRTCh. 18 - Prob. 53QRTCh. 18 - Prob. 54QRTCh. 18 - Prob. 55QRTCh. 18 - Prob. 56QRTCh. 18 - Prob. 57QRTCh. 18 - Prob. 58QRTCh. 18 - Prob. 59QRTCh. 18 - Prob. 60QRTCh. 18 - Prob. 61QRTCh. 18 - Prob. 62QRTCh. 18 - Prob. 63QRTCh. 18 - Prob. 64QRTCh. 18 - Prob. 65QRTCh. 18 - Prob. 66QRTCh. 18 - Prob. 67QRTCh. 18 - Prob. 68QRTCh. 18 - Prob. 69QRTCh. 18 - Prob. 70QRTCh. 18 - Prob. 71QRTCh. 18 - Prob. 72QRTCh. 18 - Prob. 73QRTCh. 18 - Prob. 74QRTCh. 18 - Prob. 75QRTCh. 18 - Prob. 76QRTCh. 18 - Prob. 77QRTCh. 18 - Prob. 78QRTCh. 18 - Prob. 79QRTCh. 18 - Prob. 80QRTCh. 18 - Prob. 81QRTCh. 18 - Prob. 82QRTCh. 18 - Prob. 83QRTCh. 18 - Prob. 84QRTCh. 18 - Prob. 85QRTCh. 18 - Prob. 86QRTCh. 18 - Prob. 87QRTCh. 18 - Prob. 88QRTCh. 18 - Prob. 89QRTCh. 18 - Prob. 91QRTCh. 18 - Prob. 92QRTCh. 18 - Prob. 93QRTCh. 18 - Prob. 94QRTCh. 18 - Prob. 95QRTCh. 18 - Prob. 96QRTCh. 18 - Prob. 18.ACPCh. 18 - Prob. 18.BCPCh. 18 - Prob. 18.CCPCh. 18 - Prob. 18.DCPCh. 18 - Prob. 18.ECP
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