Step 1: Analysis of Statement I
- The metallic radius of N a (neutral sodium atom) is 1.86 ̊A.
- The ionic radius of Na+ is smaller than the neutral atom because Na+ has one less electron, resulting in reduced electron-electron repulsion and greater effective nuclear charge on the remaining electrons. - Thus, Statement I is correct.
Step 2: Analysis of Statement II - While cations (Na+) are always smaller than their corresponding neutral atoms, anions (e.g., Cl-) are larger than their corresponding neutral atoms due to increased electron-electron repulsion in the outer shell.
- Hence, ions are not always smaller than the corresponding elements.
- Thus, Statement II is false.
Step 3: Conclusion - Statement I is correct, but Statement II is false.
Final Answer: (1)
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to: