B

Step 1: The frequency of the orbiting electron in a hydrogen-like atom is given by the formula:
$$ f \propto Z^{2} \cdot n^{-3} $$
Therefore, it is directly proportional to \(Z^{2}\).
Step 2: Angular momentum of the orbiting electron is quantized and proportional to quantum number \(n\):
$$ L = n \cdot \frac{h}{2\pi} \propto n $$
Thus, it is directly proportional to \(n\).
Step 3: The magnetic moment of the orbiting electron is given by:
$$ \mu \propto \frac{n}{Z} $$
Thus, it is inversely proportional to \(Z\).
Step 4: The average current due to the orbiting of an electron can be calculated but is independent of \(Z\):
$$ I = \frac{e}{T} $$
Where T is the time period which does not depend on \(Z\).
Therefore, the final matches would be:
- (i) [A] is directly proportional to \(Z^{2}\)
- (ii) [B] is directly proportional to \(n\)
- (iii) [C] is inversely proportional to \(Z\)
- (iv) [D] is independent of \(Z\)
Therefore, the correct option is B.