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Chapter 25: Problem 72

The packing fraction of a nuclide is related to the fraction of the total mass of a nuclide that is converted to nuclear binding energy. It is defined as the fraction \((M-A) / A,\) where \(M\) is the actual nuclidic mass and \(A\) is the mass number. Use data from a handbook (such as the Handbook of Chemistry and Physics, published by the CRC Press) to determine the packing fractions of some representative nuclides. Plot a graph of packing fraction versus mass number, and compare it with Figure \(25-6 .\) Explain the relationship between the two.

Short Answer

Expert verified
This exercise involves determining the packing fractions of some representative nuclides, plotting a graph of packing fraction versus mass number, and comparing it with Figure \(25-6\). The packing fraction is calculated using the formula \((M-A) / A\), where \(M\) is the actual nuclidic mass and \(A\) is the mass number. Through comparison of the graph with Figure \(25-6\), we explain the relationship between the packing fraction and the mass number.

Step by step solution

01

Understand the Packing Fraction

The packing fraction defines the fraction of the total mass of a nuclide that is converted to nuclear binding energy. It's given as \((M-A) / A\), where \(M\) represents the actual nuclide mass and \(A\) is the mass number.
02

Calculate the Packing Fractions

To calculate the packing fractions of representative nuclides, we determine the values of \(M\) and \(A\) for each nuclide from a reliable source like 'Handbook of Chemistry and Physics'. Then we substitute these values into the formula \((M-A) / A\) for each nuclide to get the packing fractions. For example, if for nuclide 1, \(M = 4\) and \(A = 2\), then the packing fraction will be \((4-2) / 2 = 1.0\). We repeat this process for all nuclides.
03

Plot the Graph

Once we have calculated the packing fractions for our representative nuclides, we proceed to plot a graph of packing fraction against mass number. This is typically done using graphing software or a spreadsheet. Using a scatter plot would be most appropriate for this task as it would allow us to clearly see the changes in packing fraction with changes in mass number.
04

Compare with Figure \(25-6\)

Upon plotting our graph, we then need to compare it with Figure \(25-6\). This requires us to analyze the differences and similarities, and explain any patterns and trends observed between our graph and Figure \(25-6\).
05

Explain the Relationship Between the Two

The final part of the exercise is understanding and explaining the correlation or relationship between our plot and Figure \(25-6\). We should look at if as the packing fraction increases, the mass number also increases in the same manner in both graphs or if there are differences, and what causes those differences.

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Most popular questions from this chapter

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