Assertion (A): The ionic radii of \( Na^+ \) and \( F^- \) are the same.
Reason (R): Both \( Na^+ \) and \( F^- \) are isoelectronic species.
(A) and (R) are correct. (R) is the correct explanation of (A)
(A) and (R) are correct, but (R) is not the correct explanation of (A)
(A) is correct but (R) is not correct
(A) is not correct but (R) is correct
Step 1: Understanding Isoelectronic Species
Isoelectronic species have the same number of electrons but different nuclear charges. Both \( Na^+ \) (11 protons, 10 electrons) and \( F^- \) (9 protons, 10 electrons) are isoelectronic. Thus, Reason (R) is correct.
Step 2: Comparing Ionic Radii of \( Na^+ \) and \( F^- \)
- \( Na^+ \) is a cation formed by losing one electron, reducing electron-electron repulsion and making it smaller than its parent atom.
- \( F^- \) is an anion formed by gaining one electron, increasing electron-electron repulsion and making it larger than its parent atom.
Since \( Na^+ \) has a smaller radius than \( F^- \), the assertion that their radii are the same is incorrect.
Step 3: Verify the Correct Answer
Since (A) is incorrect but (R) is correct, the correct answer is Option (4).
In Bohr model of hydrogen atom, if the difference between the radii of \( n^{th} \) and\( (n+1)^{th} \)orbits is equal to the radius of the \( (n-1)^{th} \) orbit, then the value of \( n \) is:
Given the function:
\[ f(x) = \frac{2x - 3}{3x - 2} \]
and if \( f_n(x) = (f \circ f \circ \ldots \circ f)(x) \) is applied \( n \) times, find \( f_{32}(x) \).
For \( n \in \mathbb{N} \), the largest positive integer that divides \( 81^n + 20n - 1 \) is \( k \). If \( S \) is the sum of all positive divisors of \( k \), then find \( S - k \).
If the real-valued function
\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]is not defined for all \( x \in (-\infty, a] \cup (b, \infty) \), then what is \( 3^a + b^2 \)?