(a) Definitions and Fission Process
Step 1 (Definitions): [1 Mark]
- Mass Defect ($\Delta m$): The difference between the sum of the masses of individual nucleons (protons and neutrons) forming a nucleus and the actual mass of the nucleus is called mass defect. $$\Delta m = [Z m_p + (A - Z) m_n] - M_{nucleus}$$
- Binding Energy (BE): The energy required to separate the nucleons of a nucleus to an infinite distance apart, or the energy released during the formation of a nucleus from its constituent nucleons. $$BE = \Delta m \times c^2$$
Step 2 (Fission Process): [0.5 Mark]
In the fission process, a heavy nucleus (high $A$) splits into two lighter nuclei of intermediate mass. The binding energy per nucleon ($BE/A$) of the heavy nucleus is lower than that of the intermediate nuclei. Since the product nuclei are more tightly bound, energy is released in the process.
(b) Numerical Calculation
Step 1 (Formula & Given Data): [0.5 Mark]
Given: $m_p = 1.007277 \text{ u}$, $m_n = 1.008665 \text{ u}$, $M_d = 2.013553 \text{ u}$.
Formula for mass defect: $\Delta m = (m_p + m_n) - M_d$
Step 2 (Mathematical Working): [0.5 Mark]
Calculation of $\Delta m$:
$$\Delta m = (1.007277 + 1.008665) - 2.013553$$ $$\Delta m = 2.015942 - 2.013553 = 0.002389 \text{ u}$$Calculation of Energy ($E$):
$$E = \Delta m \times 931.5 \text{ MeV/u}$$ $$E = 0.002389 \times 931.5$$Step 3 (Final Concluded Answer): [0.5 Mark]
Mass defect, $\Delta m = 0.002389 \text{ u}$
Energy equivalence, $E \approx 2.224 \text{ MeV}$
💡 EL10 Concept Insight: Think of the nucleus like a team of people; when they come together, they lose a tiny bit of "weight" (mass) because that energy is used to glue them together tightly. That "lost weight" is the energy that keeps the nucleus from falling apart!