Chapter 27, Problem 35QAP

To determine

(a)

The binding energy per nucleon for the given isotopes of the five least massive elements.

Explanation of Solution

Isotope	Mass (u)	Binding Energy (MeV)	BE/nucleon (MeV/nucleon)
hydrogen-1	1.007825	0.000000	0.000000
hydrogen-2	2.014102	2.224408	1.112204
hydrogen-3	3.016049	8.482184	2.827395
helium-3	3.016029	7.718359	2.572786
helium-4	4.002602	28.296925	7.074231
helium-6	6.018886	29.271267	4.878545
helium-8	8.033922	31.408115	3.926014
lithium-6	6.015121	31.995887	5.332648
lithium-7	7.016003	39.245705	5.606529
lithium-8	8.022486	41.278225	41.278225
lithium-9	9.026789	45.341402	5.037934
lithium-11	11.043897	45.548194	45.548194
beryllium-7	7.016928	7.016928	5.371660
beryllium-9	9.012174	58.172732	6.463637
beryllium-10	10.013534	64.977295	6.497730
beryllium-11	11.021657	65.482165	5.952924
beryllium-12	12.026921	68.650176	5.720848
beryllium-14	14.024866	86.707187	6.193371
boron-8	8.024605	37.739479	4.717435
boron-10	10.012936	64.751874	6.475187
boron-11	11.009305	76.205524	6.927775
boron-12	12.014352	79.575669	6.631306
boron-13	13.017780	84.453904	6.496454
boron-14	14.025404	85.423589	6.101685
boron-15	15.031100	88.189194	5.879280

Conclusion:

The binding energy per nucleon for the given isotopes of the five least massive elements is shown in the above table.

To determine

(b)

The binding energy per nucleon of the given isotopes of the five most massive naturally occurring elements.

Explanation of Solution

Isotope	Mass (u)	Binding Energy (MeV)	BE/nucleon (MeV/nucleon)
radium-221	221.01391	1701.965290	7.701200
radium-223	223.018499	1713.833455	7.685352
radium-224	224.020187	224.020187	7.680056
radium-226	226.025402	1731.617538	7.662025
radium-228	228.031064	1742.486210	7.642483
actinium-227	227.027749	1736.720262	7.650750
actinium-228	228.031015	1741.749398	7.639252
thorium-227	227.027701	1735.982519	7.647500
thorium-228	228.028716	1743.108448	7.645212
thorium-229	229.031757	1748.347170	7.634704
thorium-230	230.033127	1755.142419	7.631054
thorium-231	231.036299	1760.259116	7.620169
thorium-232	232.038051	1766.698534	7.615080
thorium-234	234.043593	1777.678985	7.596919
protactinium-231	231.035880	1759.866957	7.618472
protactinium-234	234.043300	1777.169458	7.594741
uranium-231	231.036264	1758.726808	7.613536
uranium-232	232.037131	1765.990598	7.612028
uranium-233	233.039630	1771.734190	7.604009
uranium-234	234.040946	1778.579740	7.600768
uranium-235	235.043924	1783.877146	7.590967
uranium-236	236.045562	1790.422754	7.586537
uranium-238	238.050784	1801.701284	7.570173
uranium-239	239.054290	1806.506861	7.558606

Conclusion:

The binding energy per nucleon of the given isotopes of the five most massive naturally occurring elements is shown in table above.

To determine

(c)

The comparison for the binding energy per nucleon of the given isotopes of the five most massive naturally occurring elements and the binding energy per nucleon for the given isotopes of the five least massive elements and also comment on the pattern or trends that are obvious.

Explanation of Solution

The lighter elements have $\frac{EB}{nucleon}$ values that vary radically and stay much less than the maximum of $8.79MeV/nucleon$ at ${}_{26}^{56}Fe.$ The heavier elements have $\frac{EB}{nucleon}$ values that are very stable and stay right near the maximum value of $8.79MeV/nucleon$.

Conclusion:

Thus, lighter elements stay much less than $8.79MeV/nucleon$ and the heavier elements are stable and near the maximum value of $8.79MeV/nucleon$.