Definition: Binding energy of a nucleus is defined as the energy required to separate the nucleons (protons and neutrons) of a nucleus to an infinite distance from each other, or equivalently, the energy released when nucleons are bound together to form a nucleus.
Step 1 (Formula & Given Data): [1 Mark]
The energy released ($Q$) in a nuclear fission reaction is given by the difference between the total binding energy of the product nuclei and the total binding energy of the parent nucleus:
$$Q = (\text{Total BE of products}) - (\text{Total BE of parent})$$Given data:
- Parent nucleus: $A_p = 240$, $\frac{BE}{A} = 7.6 \text{ MeV}$
- Product nuclei (two fragments): $A_f = 120$, $\frac{BE}{A} = 8.5 \text{ MeV}$
Step 2 (Step-by-Step Mathematical Working): [1.5 Marks]
First, calculate the total binding energy of the parent nucleus ($BE_p$):
$$BE_p = 240 \times 7.6 \text{ MeV} = 1824 \text{ MeV}$$Next, calculate the total binding energy of the two product nuclei ($BE_f$):
$$BE_f = 2 \times (120 \times 8.5 \text{ MeV})$$ $$BE_f = 2 \times 1020 \text{ MeV} = 2040 \text{ MeV}$$Now, calculate the energy released ($Q$):
$$Q = BE_f - BE_p$$ $$Q = 2040 \text{ MeV} - 1824 \text{ MeV}$$Step 3 (Final Concluded Answer): [0.5 Mark]
$$Q = 216 \text{ MeV}$$The energy released in the fission process is 216 MeV.
💡 EL10 Concept Insight: Think of binding energy like the "glue" holding the nucleus together; when a big, unstable nucleus breaks into two smaller, more stable pieces, the new pieces are held together much more tightly, so the "extra" glue that isn't needed anymore is released as pure energy.