Question

Arrange the following elements in the increasing order of their binding energies per nucleon.
A. \(^{4}\text{He}\)
B. \(^{6}\text{Li}\)
C. \(^{14}\text{N}\)
D. \(^{12}\text{C}\)

Choose the correct answer from the options given below:

• A. A, B, C, D
• B. A, B, D, C
• C. B, A, C, D
• D. B, A, D, C

Hint:

Recall the values: Li-6 about 5.3, He-4 about 7.1, N-14 about 7.5, C-12 about 7.7 MeV per nucleon.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Binding energy per nucleon shows how tightly a nucleus is held together. We must list the four nuclei from the lowest value to the highest.

Step 2: Key Approach:
We use the known binding energy per nucleon values from the binding energy curve.
He-4: about 7.07 MeV.
Li-6: about 5.33 MeV.
N-14: about 7.48 MeV.
C-12: about 7.68 MeV.

Step 3: Arrange:
Lowest is Li-6 (B), then He-4 (A), then N-14 (C), then C-12 (D).
So the increasing order is B, A, C, D.

Step 4: Why These Values Make Sense:
Helium-4 is unusually stable for its size, so it sits above Li-6, which is a loosely bound light nucleus. C-12 is a very stable nucleus and N-14 is slightly lower. For light nuclei the curve is not smooth, so these values must be remembered.

Step 5: Checking Each Option:
Option 1 (A, B, C, D) puts He below Li, which is wrong.
Option 2 (A, B, D, C) has the same mistake and also swaps C and D.
Option 3 (B, A, C, D) matches our order. Correct.
Option 4 (B, A, D, C) swaps N-14 and C-12. Wrong.

Final Answer:
The increasing order of binding energy per nucleon is Li-6, He-4, N-14, C-12, which is option 3. \[ \boxed{B, A, C, D} \]