Which of the following figures correctly represent the shape of the curve of binding energy per nucleon as a function of mass number?

Question

A \(7.9\ \text{MeV}\) \(\alpha\)-particle scatters from a target material of atomic number \(79\). From the given data, the estimated diameter of the nuclei of the target material is (approximately) _________ m. \[ \left[\frac{1}{4\pi\varepsilon_0}=9\times10^9\ \text{Nm}^2\text{/C}^2 \text{ and electron charge }=1.6\times10^{-19}\ \text{C}\right] \]

Answer 1

Nucleus stability is quantified by binding energy per nucleon, which typically follows a trend with mass number. This trend is characterized as follows:

For nuclei with mass numbers below 20, binding energy per nucleon exhibits a steep increase.
A peak in the binding energy per nucleon curve occurs in the medium mass number range, around iron, signifying maximum nuclear stability in this region.
Beyond this peak, the binding energy per nucleon shows a gradual decline for heavier nuclei due to escalating proton-proton repulsion.

This behavior traces a curve that begins low for very light nuclei, ascends to a peak at intermediate mass numbers, and subsequently declines for heavier elements. Based on this information, the option that accurately depicts the binding energy per nucleon as a function of mass number is:

Which of the following figures correctly represent the shape of the curve of binding energy per nucleon as a function of mass number?

Show Hint

The Correct Option is B

Solution and Explanation

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