Show that the parking factor of a nucleus is maximum when binding energy is zero

Packing factor of a nucleus is the ratio of mass defect and the mass number defined as,

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Whereas binding energy is the energy that holds the nucleons together in a nucleus. It is equal to the mass defect of the nucleus.

Thus, lower the packing fraction, greater is the binding energy and the nucleus is more stable.

When the binding energy is zero, the isotopic mass is greater than the mass number. In this case, the packing factor of the nucleus is maximum.

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.