Question

Define binding energy (BE) of a nucleus. An unstable nucleus has mass number A = 240 and \(\dfrac{BE}{A} = 7.6\) MeV. It splits in two fragments, each of A = 120 with \(\dfrac{BE}{A} = 8.5\) MeV. Calculate the energy released.

Hint:

Binding energy is the energy needed to break a nucleus into free nucleons. Energy released = \(2 \times 120 \times 8.5 - 240 \times 7.6 = 216\ \text{MeV}\).

Answer 1

Step 1: Define binding energy:
The binding energy of a nucleus is the minimum energy needed to separate it into its free, individual nucleons. It equals the energy equivalent of the mass defect, \(\Delta m\,c^2\).

Step 2: Idea of the calculation:
Energy is released when nucleons end up in nuclei with a larger total binding energy. So the energy released equals (total BE of the fragments) minus (total BE of the parent).

Step 3: Binding energy of the parent:
\(BE = A \times (BE/A) = 240 \times 7.6 = 1824\ \text{MeV}\).

Step 4: Binding energy of the fragments:
Each fragment: \(120 \times 8.5 = 1020\ \text{MeV}\).
Two fragments: \(2 \times 1020 = 2040\ \text{MeV}\).

Step 5: Energy released:
\[ Q = 2040 - 1824 = 216\ \text{MeV} \]

Final Answer:
The energy released is 216 MeV. \[ \boxed{Q = 216\ \text{MeV}} \]