Statement - I : Greater is the mass of nucleus, more will be its binding energy.
Statement - II : Nucleus with less $\frac{BE}{A}$ (Binding energy/nucleon) breaks into nucleus with higher $\frac{BE}{A}$.
Choose the correct option :
Statement - II : Nucleus with less $\frac{BE}{A}$ (Binding energy/nucleon) breaks into nucleus with higher $\frac{BE}{A}$.
Choose the correct option :
Show Hint
- Statement I is true & statement II is false
- Statement I is false & statement II is true
- Both are true
- Both are false
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
This is a statement-based question dealing with the concepts of nuclear binding energy (BE) and binding energy per nucleon ($BE/A$). We need to evaluate the truthfulness of both statements.
Step 3: Detailed Explanation:
Statement - I: Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. Since binding energy roughly scales with the number of nucleons (A), a nucleus with a greater mass (higher A) generally has a greater total binding energy. Even though the binding energy *per nucleon* drops for heavy nuclei (A $>$ 60), the *total* binding energy continues to increase with mass. Therefore, Statement I is generally True.
Statement - II: Nuclear stability is determined by the binding energy per nucleon ($BE/A$). A higher $BE/A$ means the nucleus is more tightly bound and therefore more stable. Nuclei with low $BE/A$ (very light or very heavy nuclei) tend to undergo nuclear reactions (fusion or fission) to form nuclei with higher $BE/A$, releasing energy in the process. Therefore, Statement II is True.
Since both Statement I and Statement II are correct in the context of nuclear physics, the correct option is (C).
Step 4: Final Answer:
Both Statement I and Statement II are true.
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