   Chapter 25, Problem 38PS

Chapter
Section
Textbook Problem

Calculate the binding energy per mole of nucleons for nitrogen-14. The mass of nitrogen-14 is 14.003074.

Interpretation Introduction

Interpretation: The binding energy per mole of nucleons for nitrogen-14 has to be calculated.

Concept introduction:

Binding energy is the energy required to separate the nucleus of an atom into proton and neutron. Binding energy is given by Eb=Δm×(c)2, where Δm is the mass defect and c is the velocity of light =3×108m/sec-1

Mass defect is the sum of the masses of the individual nucleons that form an atomic nucleus and the mass of the nucleus.

Binding energy per nucleon =TotalbindingenergyofnucleusNumberofnucleonsinthenucleus

Explanation

Given,

The mass of calcium-40=39.962589

The mass of proton=1.00783

The mass of neutrons=1.00867

Number of proton=7=7×1.00783=7.05481

Number of neutron=7= 7×1.00867=7.06069

Masses of the individual nucleons=7.05481+7.06069=14.1155

The mass of nitrogen-14 is 14.003074.

Mass defect Δm=Mm

Δm=Mm=14.115514.003074=14.0030Δm=0.1125g/mol=1.125×104kg/mol

Binding energy:

Eb=Δm×(c)2=  1.125×10-4kg/mol×(3×108m/s)2=1.0125×1013J=1.0125×1010kJ

The binding energy for nitrogen-14 is 1

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