# Given the following information: Mass of proton = 1.00728 u Mass of neutron = 1.00866 u Mass of electron = 5.486 × 10 −4 u Speed of light = 2.9979 × 10 8 m/s Calculate the nuclear binding energy of M 12 24 g , which has an atomic mass of 23.9850 u.

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 77CWP
Textbook Problem
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## Given the following information:Mass of proton = 1.00728 uMass of neutron = 1.00866 uMass of electron = 5.486 × 10−4 uSpeed of light = 2.9979 × 108 m/sCalculate the nuclear binding energy of M 12 24 g , which has an atomic mass of 23.9850 u.

Interpretation Introduction

Interpretation: The nuclear binding energy of 1224Mg is to be calculated.

Concept introduction: The sum of the masses of the component nucleons and the actual mass of a nucleus is known as the mass defect and it can be used to calculate the nuclear binding energy.

To determine: The nuclear binding energy of 1224Mg .

### Explanation of Solution

Explanation

Given

The atomic mass of 1224Mg=23.9850amu

The mass of a neutron is 1.0087amu .

The mass of a proton is 1.00782amu .

Number of protons in 1224Mg=12

Number of neutrons in 1224Mg=12

The mass defect is calculated by the formula,

Δm=Atomicmass of 1224Mg[Numberofprotons×massof11HprotonNumberofneutrons×massofneutron]

Substitute the value of the atomic mass of 1224Mg , the number of protons and mass of the 11H proton and that of the neutron in the above equation.

Δm=23.9850[(12×1.00782)+(12×1.0087)]Δm=0.21324amu/nucleus

The conversion of amu/nucleus to Kg/nucleus is done as,

1amu=1.66×1027Kg

Therefore, the conversion of 0.589amu/nucleus into kg/nucleus is,

2.38×103amu/nucleus=(0.21324×1.66×1027)kg/nucleus=-3.5397×10-28Kg/nucleus_

Therefore, the mass defect (Δm') of 1224Mg is -3

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