Consider the following statements (A) and (B) and identify the correct answer given below.
Statement (A) : Positive values of packing fraction implies a large value of binding energy.
Statement (B) : The difference between the mass of the nucleus and the mass number of the nucleus is called packing fraction

(A) and (B) are false

Understand Packing Fraction

Packing fraction is a concept used in nuclear physics to understand how tightly bound the nucleons (protons and neutrons) are within a nucleus. It is mathematically defined as:

Packing Fraction = (Actual isotopic mass - Mass number) / Mass number

Where:

• Actual isotopic mass: The precise mass of a specific isotope of an element, measured in atomic mass units (amu).
• Mass number (A): The total number of protons and neutrons in the nucleus.

Analyzing the Statements

1. Statement (A):

• Positive packing fraction values occur when the actual isotopic mass exceeds the mass number, indicating less mass defect.
• Binding energy is directly proportional to the mass defect (the "missing" mass converted into binding energy). A lower mass defect leads to lower binding energy.
• Hence, a positive packing fraction does NOT imply a large value of binding energy. Instead, a negative packing fraction indicates greater binding energy due to a higher mass defect.

2. Statement (B):

• The difference between the actual isotopic mass and the mass number is part of the numerator in the packing fraction formula. However, the packing fraction is normalized by dividing this difference by the mass number.
• Simply stating the difference as the packing fraction is an incomplete definition.

Statement (B) is incorrect.

• Both Statement (A) and Statement (B) are incorrect.
• The correct definition of packing fraction is:

Packing Fraction = (Actual isotopic mass - Mass number) / Mass number

A negative packing fraction indicates a higher binding energy and greater nuclear stability.