   Chapter 19, Problem 44E

Chapter
Section
Textbook Problem

# The most stable nucleus in terms of binding energy per nucleon is 56Fe. If the atomic mass of 56Fe is 55.9349 u, calculate the binding energy per nucleon for 56Fe.

Interpretation Introduction

Interpretation: The binding energy per nucleon of 56Fe is to be calculated.

Concept introduction: The sum of 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 binding energy per nucleon of 56Fe

Explanation

Explanation

The atomic mass of 56Fe=55.9349amu .

Mass of 11H=1.00782 amu .

The mass of neutron is 1.00866amu .

Number of protons in 56Fe=26

Number of neutrons in 56Fe=30

The mass defect is calculated by the formula,

Δm=Atomicmass of 56Fe [Numberofprotons×massof11HprotonNumberofneutrons×massofneutron]

Substitute the value of the atomic mass 56Fe  , the number of protons and mass of the 11H proton and that of the neutron in the above equation.

Δm=55.9349[(26×1.00782)+(30×1.00866)]Δm=0.589amu/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,

0.5289amu/nucleus=(0.5289×1×1.66×1027)kg/nucleus=-0.8779×10-27Kg/nucleus_

Therefore, the mass defect (Δm) of 56Fe is -0

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