Question

The binding energy per nucleon of \( ^{16}\text{O} \) is \( 7.97 \) MeV and that of \( ^{17}\text{O} \) is \( 7.75 \) MeV. The energy in MeV required to remove a neutron from \( ^{17}\text{O} \) is

• A. $3.52$
• B. $3.64$
• C. $4.23$
• D. $7.86$
• E. $1.68$

Hint:

Separation energy = difference of total binding energies, NOT per nucleon.

Answer 1

The Correct Option is C

Concept: Neutron separation energy
Energy required to remove one neutron from a nucleus is called neutron separation energy: \[ S_n = B(^{17}\text{O}) - B(^{16}\text{O}) \] where $B$ = total binding energy.

Step 1: Calculate total binding energies
Binding energy = (binding energy per nucleon) × (number of nucleons) \[ B(^{17}\text{O}) = 17 \times 7.75 = 131.75 \text{ MeV} \] \[ B(^{16}\text{O}) = 16 \times 7.97 = 127.52 \text{ MeV} \]

Step 2: Apply separation energy formula \[ S_n = B(^{17}\text{O}) - B(^{16}\text{O}) \] \[ S_n = 131.75 - 127.52 \] \[ S_n = 4.23 \text{ MeV} \]

Step 3: Important physical interpretation

• This is the energy needed to remove the last neutron
• If binding energy per nucleon decreases → nucleus is less tightly bound
• $^{17}$O is less stable per nucleon than $^{16}$O \[ \boxed{4.23 \text{ MeV}} \] So correct answer is actually: \[ \boxed{(C)} \] Final Answer: \[ \boxed{4.23 \text{ MeV}} \]