Question

The packing fraction of elements A, B and C are -20, -27 and 18 respectively. Arrange them in increasing order of stability.
A. C < A < B
B. A < B < C
C. A < C < B
D. None of the above

Answer 1

Hint: The value of packing fraction depends upon the manner of packing of the nucleons within the nucleus. Its value can be negative, positive or even zero. A negative packing fraction generally indicates stability of the nucleus.

Step-by-Step Solution:
Before we move on to the solution of this question, we must first define what ‘packing fraction’ really means.
Packing fraction of an element is given by the formula:

Mass\text{ }number \\\ \end{matrix}}~\times \text{ }{{10}^{4}}$$ Packing Fraction can have positive, negative or zero value. Zero value of packing fraction is found in mono isotopic elements where the isotopic mass is equal to the mass number. Negative value of packing fraction indicates that there is mass defect, hence binding energy. Such nuclei are stable. Positive values of Packing fraction are unstable undergoing fission and fusion processes. eg. 11H (+ve packing fraction) undergoes fusion while 235U (+ve packing fraction) undergoes fission. The stability of an atom appears to depend on the relative number of protons and neutrons present in the nucleus. Elements having mass number in the range of (40 - 120) have a high binding energy per nucleon and hence greater stability. On the other hand, heavy elements have very low binding energy per nucleon and have unstable nuclei. Thus, from this analysis, we can conclude that the more negative the packing fraction of an element, the higher is its bond energy thereby resulting in greater stability. Therefore, ranking the given elements in order of stability: C < A < B. Therefore, the answer to this question is a). Note: While just knowing that the more negative the packing fraction, the higher the stability would be enough on the surface level for you to be able to answer this question, it is highly advisable that you learn how this relation is obtained. This is to ensure that all your basic concepts are thoroughly covered which in turn ensure that you’re able to navigate through future topics more easily.