Question

which of the following radii comparisons is correct?
a. ( n^{3 - } < n )
anions are always larger than the neutral atom from which they are derived.
b. ( ti^{2 + } > ti^{3 + } )
c. ( in^{3 + } < in^{+} )
d. ( c^{4 + } > c^{4 - } )
e. ( as^{5 - } < as^{3 + } )

Explanation:

• For ions, when comparing radii:
• Anions (\(N^{3 -}\)) have more electrons than the neutral atom (\(N\)). The extra electrons increase electron - electron repulsion, causing the anion to be larger than the neutral atom. So \(N^{3 -}>N\), option A is incorrect.
• For cations with the same element (\(Ti^{2 +}\) and \(Ti^{3+}\)), as the charge increases (more electrons are removed), the effective nuclear charge acting on the remaining electrons increases. This pulls the electrons closer to the nucleus. So \(Ti^{2+}>Ti^{3 +}\), option B is correct.
• For \(In^{3+}\) and \(In^{+}\), \(In^{3+}\) has lost more electrons. The higher positive charge on \(In^{3+}\) means a greater effective nuclear charge. So \(In^{3+}
• For \(C^{4+}\) and \(C^{4 -}\), \(C^{4+}\) has lost electrons (smaller radius due to higher effective nuclear charge) and \(C^{4 -}\) has gained electrons (larger radius due to electron - electron repulsion). So \(C^{4+}
• For \(As^{5 -}\) and \(As^{3+}\), \(As^{5 -}\) is an anion (gained electrons, larger radius) and \(As^{3+}\) is a cation (lost electrons, smaller radius). So \(As^{5 -}>As^{3+}\), option E is incorrect.

Answer:

B. \(Ti^{2+}>Ti^{3 +}\), C. \(In^{3+}