This binding energy per nucleon for the parent nucleus is `E_(1)` and that for the daughter nuclei is `E_(2)`. Then

Options

A. (a)`E_2 = 2E_1`
B. (b)`E_1 gt E_2`
C. (c)`E_2 gt E_1`
D. (d)`E_1 = E_2`

Answer

To solve the problem regarding the binding energy per nucleon for the parent nucleus and the daughter nuclei, we can follow these steps:

### Step 1: Understand the Concept of Binding Energy
Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. The binding energy per nucleon gives us an idea of the stability of a nucleus. A higher binding energy per nucleon indicates a more stable nucleus.

### Step 2: Define the Parent and Daughter Nuclei
Let’s denote:
- The parent nucleus as A (with binding energy per nucleon E1).
- The daughter nuclei as B and C (with binding energy per nucleon E2).

### Step 3: Analyze the Decay Process
In a nuclear decay process, a parent nucleus (A) transforms into daughter nuclei (B and C). This process typically results in the release of energy, indicating that the daughter nuclei are more stable than the parent nucleus.

### Step 4: Compare Binding Energies
Since the daughter nuclei (B and C) are formed from the decay of the parent nucleus (A), and they are more stable, we can conclude that the binding energy per nucleon for the daughter nuclei (E2) will be greater than that of the parent nucleus (E1). Therefore, we can write:
\[ E2 > E1 \]

### Step 5: Conclusion
From our analysis, we find that the correct relationship between the binding energies is:
\[ E2 > E1 \]

### Final Answer
The correct relation is that the binding energy per nucleon for the daughter nuclei (E2) is greater than that for the parent nucleus (E1).