Chapter 25, Problem 35PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Calculate the binding energy per mole of nucleons for calcium-40, and compare your result with the value in Figure 25.4. Masses needed for this calculation are (in g/mol) H 1 1 = 1.00783, n 0 1 = 1.00867, and C 20 40 a = 39.96259.Figure 25.4 Relative stability of nuclei. Binding energy per nucleon for the most stable isotope of elements between hydrogen and uranium is plotted as a function of mass number. (Fission and fusion are discussed in Sectionc25.6.)

Interpretation Introduction

Interpretation:

Binding energy per nucleon for calcium-40 has to be calculated and the result has to be compared with the figure

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

Masses of the individual nucleons,

=20Ã—1.00783=20.1566

=20Ã—1.00867=20.1734

=20.1566+20.1734=40.33

The mass of the nucleus =39.96259

Mass defect Î”m=Mâˆ’m

Î”m=40.33-39.96259=0.367411g/molÎ”m=0.367411Ã—10âˆ’3kg/mol=3.67Ã—10âˆ’4kg/mol

Binding energy:

Eb=Î”mÃ—(c)2=Â Â 3.67Ã—10âˆ’4kg/molÃ—(3Ã—108m/s)2=3.306Ã—1013J=3.306Ã—1010kJ

The binding energy for calcium-40 =3

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