Question

Make inferences from the binding energy per nucleon curve, as shown:

• A. It's more difficult to take a nucleon out from ${}^{238}U$ ,then ${}^{56}Fe$
• B. It's more difficult to take a nucleon out from ${}^{6}Li$ than from ${}^{4}He$
• C. If a ${}^{238}U$ nucleus somehow disintegrates into nuclei of smaller mass numbers (between 75 – 238), energy will be released
• D. If a ${}^{16}O$ nucleus somehow disintegrates into nuclei of smaller mass numbers, energy will be released.

Answer 1

The correct option is C If a ${}^{238}U$ nucleus somehow disintegrates into nuclei of smaller mass numbers (between 75 – 238), energy will be released

The binding energy per nucleon $\left({\Delta }_{b/n}\right)$ gives us a rough idea of average binding energy per nucleon.Higher total binnding energy means that nuclei is more bound.

If ${}^{238}U$ breaks down into smaller nuclei with $A$ between 75-238, we can see the product nuclei will have higher $\frac{B}{A}$
Uranium has a lower binding energy, so to split all its nucleons apart you will have to give some small energy(comparatively). Now from those free nucleons if smaller nuclei are made which have higher binding energy then energy will be released, that too higher than what was provided to break uranium. This process will therefore release energy
If ${}^{16}O$ was to break up into smaller mass numbers, we see from the graph that any nucleus below ${}^{16}O$has lesser $\frac{B}{A}$ This process therefore will absorb a lot of energy (if available; otherwise won't occur at all), and not release energy.