In a fission process, nucleus `A` divides into two nuclei `B` and `C`, their binding energies being `E_a, E_b` and `E_c` respectively. Then.

Options

A. `E_b+E_cgt E_a`
B. `E_b+E_c lt E_a`
C. `E_b +E_c =E_a`
D. `E_b-E_c=E_a`

Answer

To solve the problem regarding the fission process where nucleus A divides into two nuclei B and C, we need to analyze the binding energies involved. Here’s the step-by-step solution:

### Step 1: Understand Binding Energy
The binding energy of a nucleus is the energy required to disassemble it into its constituent nucleons. A higher binding energy per nucleon indicates a more stable nucleus.

### Step 2: Analyze the Fission Process
In a fission reaction, a heavy nucleus (A) splits into two lighter nuclei (B and C). This process typically releases a significant amount of energy because the binding energy per nucleon of the products (B and C) is greater than that of the original nucleus (A).

### Step 3: Write the Energy Relationship
The energy released (Q value) in the fission process can be expressed as:
\[ Q = (E_A - (E_B + E_C)) \]
Where:
- \( E_A \) is the binding energy of nucleus A.
- \( E_B \) is the binding energy of nucleus B.
- \( E_C \) is the binding energy of nucleus C.

### Step 4: Determine the Sign of Q
Since energy is released in the fission process, the Q value is positive. This implies:
\[ E_A < E_B + E_C \]
This means that the binding energy of the original nucleus A is less than the total binding energy of the two resulting nuclei B and C.

### Step 5: Conclusion
From the above analysis, we conclude that:
\[ E_A < E_B + E_C \]
This indicates that the binding energy of the original nucleus A is less than the sum of the binding energies of the two fission products B and C.

### Final Answer
Thus, the correct relationship is:
\[ E_A < E_B + E_C \]

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