In Hideki Yukawa's meson field theory, the nuclear force between two nucleons at intermediate distances ($r \sim 1-2\text{ fm}$) is primarily mediated by the exchange of
### Step-by-Step Derivation & Verification: 1. **Uncertainty Principle Formulation**: A virtual particle of mass $m$ can be emitted and reabsorbed within time $\Delta t \approx \frac{\hbar}{\Delta E} = \frac{\hbar}{m c^2}$. 2. **Range of Interaction**: $R \approx c \Delta t = \frac{\hbar}{m c}$ 3. **Physical Identification**: To achieve the observed nuclear interaction range of $R \approx 1.4\text{ fm}$, Yukawa predicted a mediating particle with mass $\approx 140\text{ MeV}/c^2$, later discovered as the $\pi$-meson (pion). 4. **Conclusion**: Pions. Option (A) is correct.