---
title: "The graph shows the average binding energy per nucleon, \\(E_b / A\\), as a function of mass number \\(A\\) for naturally occurring nuclei. Based on the graph, which of the following statements correctly explains how changes in binding energy per nucleon determine whether a nuclear reaction releases energy?"
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url: "https://nerd-notes.com/ubq/123535/"
date_modified: "2026-09-28T12:00:04+00:00"
---

# The graph shows the average binding energy per nucleon, \(E_b / A\), as a function of mass number \(A\) for naturally occurring nuclei. Based on the graph, which of the following statements correctly explains how changes in binding energy per nucleon determine whether a nuclear reaction releases energy?

The graph shows the average binding energy per nucleon, \(E_b / A\), as a function of mass number \(A\) for naturally occurring nuclei. Based on the graph, which of the following statements correctly explains how changes in binding energy per nucleon determine whether a nuclear reaction releases energy?

![A 2D Cartesian graph with a horizontal axis labeled Mass number, A spanning from 0 to 260 with tick marks at 0, 50, 100, 150, 200, 250 and a vertical axis labeled Binding energy per nucleon, E_b / A (MeV/nucleon) spanning from 0 to 10 with tick marks at 0, 2, 4, 6, 8, 10. A smooth, solid curve begins near (1, 1.1), rises steeply through points near (4, 7.1) and (12, 7.7), reaches a peak at approximately (56, 8.8), and then gently decreases with a slight downward slope through (120, 8.5) and ends near (238, 7.6). A vertical dashed line extends from the horizontal axis at A = 56 up to the peak of the curve, labeled ^{56}Fe near the peak. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596803-fonrzp.jpg)

- **A.** Fusing two nuclei with \(A \approx 100\) to form a single nucleus with \(A \approx 200\) releases energy because the total binding energy of a nucleus always increases with increasing mass number.
- **B.** Both the fusion of two light nuclei with \(A < 20\) and the fission of a heavy nucleus with \(A > 200\) produce nuclei with higher binding energy per nucleon, resulting in a decrease in total rest mass and a release of energy.
- **C.** Nuclei near the peak at \(A \approx 56\) have the greatest rest mass per nucleon, so splitting an iron nucleus into two lighter fragments releases the greatest amount of energy per nucleon.
- **D.** The steep positive slope of the curve for \(A < 56\) indicates that splitting a light nucleus such as Carbon-12 into lighter fragments releases more energy per nucleon than the fission of Uranium-235.

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