Question

Let the binding energy per nucleon of nucleus be denoted by \( E_{bn} \) and radius of the nucleus by \( r \). If mass numbers of nuclei A and B are 64 and 125 respectively, then

• A. \( r_A < r_B \)
• B. \( r_A > r_B \)
• C. \( E_{bnA} > E_{bnB} \)
• D. \( E_{bnA} < E_{bnB} \)

Hint:

Nuclear trends: \begin{itemize} \item Radius \( \propto A^{1/3} \). \item Binding energy per nucleon peaks near Fe. \end{itemize}

Answer 1

The Correct Option is A

Concept 1: Nuclear radius \[ r = r_0 A^{1/3} \] Since: \[ A_B > A_A \Rightarrow r_B > r_A \] So: \[ r_A < r_B \] Option (A) correct. Concept 2: Binding energy per nucleon Binding energy per nucleon peaks near iron (\( A\approx56 \)) and decreases for heavier nuclei. Since: \[ 64 \text{ is closer to peak than } 125 \] \[ E_{bnA} > E_{bnB} \] Option (C) correct.