Question

Packing fraction, an informative method previously used to decide stability of a nucleus is given by $Packing\,fraction=\dfrac{^{A}{{M}_{Z}}-A}{A}\times {{10}^{-4}}$, where $^{A}{{M}_{Z}}$is actual mass of nuclide in amu and a is the mass number. Which of the statements are correct about packing fraction?
A. A nuclide with negative packing fraction has an atomic mass $^{A}{{Z}_{M}}$ less than its mass number.
B. A nuclide with zero packing fraction has an atomic mass $^{A}{{Z}_{M}}$equal to its mass number.
C. A nuclide with a positive packing fraction has an atomic mass $^{A}{{Z}_{M}}$ more than its mass number.
D. More is the magnitude of negative packing fraction, more will be the stability of the nucleus.

Answer 1

Hint: Check each option carefully, by using the conditions of every option in the question. Then find out the sign of the packing fraction in each case and find the correct options.

Complete answer:
In order to answer our question, we need to learn about packing a fraction of a nucleus. Packing fraction gives us an idea about the orientation of the nucleons that are arranged in the nucleus. It is the ratio of the mass defect to the number of nucleons. Now, we have been given the formula of the packing fraction and with the help of that, we will check the options one by one and get to the answer. The formula for the packing fraction is given by:
\[P=\dfrac{^{A}{{Z}_{M}}-A}{A}\times {{10}^{4}}\]
Now, we will use approximation to come to a result. In option A, it is given that $MIf we put mass number and atomic number equal in the equation, then the numerator becomes 0, and so, the overall packing fraction becomes 0 too. Hence option B is correct .
Similar to option A, if we put $M>A$, then we get the overall packing fraction to be positive, which makes option C also correct.
Generally, packing fraction is used to determine the stability of a nucleus. More is the packing fraction, more will be the stability of the compound, this makes option D also correct.

So, all the options, i.e A,B,C and D are correct, which is the answer for the question.

Note:
It is to be noted that as the packing fraction becomes more, in a nucleus, then the nucleus loses all its extra energy, and this is the reason for the stability.