The compound unstabel nucleus `._(92)^(236)U` often decays in accordance with the following reaction
`._(92)^(236)U rarr ._(54)^(140)Xe +._(38)^(94)Sr ` + other particles
During the reaction, the uranium nucleus ''fissions'' (splits) into the two smaller nuceli have higher nuclear binding energy per nucleon (although the lighter nuclei have lower total nuclear binding energies, because they contain fewer nucleons).
Inside a nucleus, the nucleons (protonsa and neutrons)attract each other with a ''strong nuclear'' force. All neutrons exert approxiamtely the same strong nuclear force on each other. This force holds the nuclear are very close together at intranuclear distances.
Which of the following graphs might represent the relationship between atomic number (i.e., ''atomic weight'') and the total binding energy of the nucleus, for nuclei heavier than `._(38)^(94)Sr` ?

Options

A.
B.
C.
D.

Answer

c

Explanation

Graph (a) would correcrtly show the binding energy per nucleons, but this differs from the total binding energy of the nucleus. The total binding energy takes into account not only the binding energy takes into account not only the binding energy per nucleon, but also the number of nucleons.
To understand this subtle point, compare `._(38)^(94)Sr` to `._(32)^(236)U`. As the passage states, `._(38)^(94)Sr` has a higher binding energy per nucleon. Here,
`._(38)^(94)Sr` binding enrgy per nucleon `~~ 9MeV`
`._(32)^(236)U` binding enrgy per nucleon `~~ 7MeV`
But `._(32)^(236)U` still has a higher total binding energy, simply because it contaisn more nucleons. Indeed, since total binding energy of a nucleus=binding energy per nucleon `xx`number of nuclei, the total binding energies are
`._(38)^(94)Sr xx (94 nucleons)~~846 MeV`
`._(32)^(236)U xx (236 nucleons) ~~1650 MeV`
So, as atomic mass increase linearly with atomic mass. It incerease at a smaller and smaller rate, precisely because the binding energy per nucleon decreases. Indeed, since 'atomic mass number' specifies the number of necleons, the binding energy per nucleon is simply the slope of a binding energy vs. atomic mass number graph. Between strontium and uranium, this slope decrease, as just explained. Thus, the answer must be (c) rather than (d).