Question

Nuclei A and B form a nucleus C. BE/N for A, B and C are 3 MeV, 7 MeV and 6 MeV. Then energy produced in
\[ 2A^3 + B^4 \rightarrow C^{10} \]

• A. 8 MeV
• B. 12 MeV
• C. 10 MeV
• D. 14 MeV

Hint:

In nuclear reactions, energy is released when the final nucleus has greater total binding energy than the initial nuclei. Always convert BE/N into total binding energy first by multiplying it with the mass number.

Answer 1

The Correct Option is D

Step 1: Understand the meaning of BE/N.
BE/N means binding energy per nucleon. To find the total binding energy of a nucleus, we multiply the binding energy per nucleon by its mass number.
For the given nuclei:
\[ \text{For } A^3,\quad \text{Total BE} = 3 \times 3 = 9 \text{ MeV} \] \[ \text{For } B^4,\quad \text{Total BE} = 7 \times 4 = 28 \text{ MeV} \] \[ \text{For } C^{10},\quad \text{Total BE} = 6 \times 10 = 60 \text{ MeV} \] Step 2: Find the total initial binding energy.
In the reaction, two nuclei of \( A^3 \) and one nucleus of \( B^4 \) combine to form one nucleus of \( C^{10} \).
So, the total initial binding energy is:
\[ \text{Initial BE} = 2 \times 9 + 28 \] \[ = 18 + 28 = 46 \text{ MeV} \] Step 3: Find the final binding energy.
The final nucleus formed is \( C^{10} \), whose total binding energy is:
\[ \text{Final BE} = 60 \text{ MeV} \] Step 4: Calculate the energy produced.
Energy released in a nuclear reaction is equal to the increase in total binding energy.
\[ \text{Energy produced} = \text{Final BE} - \text{Initial BE} \] \[ = 60 - 46 = 14 \text{ MeV} \] Thus, the reaction releases \( 14 \text{ MeV} \) of energy.
Final Answer: 14 MeV.