Fracture toughness comes from the stress intensity relation \( K = Y \sigma \sqrt{\pi a} \), so its units fall straight out of the units already sitting on the right side of that formula. Stress \( \sigma \) is measured in megapascals, and crack length \( a \) is measured in metres, so the square root term contributes a factor of \( \text{m}^{1/2} \). Multiplying stress by this square root of length gives units of \( \text{MPa}\cdot\text{m}^{1/2} \), not squared metres, not plain pascals, and nothing resembling energy per mole. So fracture toughness is reported in \( \text{MPa}\cdot\text{m}^{1/2} \), option (B).