Match List I with List II. List I List II (A) 2^ nd orbit of H (I)...

The radius of the $n^{\text{th}}$ Bohr orbit of a hydrogen-like species is given by:
$r_n = a_0 \dfrac{n^2}{Z}$

(A) For the $2^{\text{nd}}$ orbit of H ($n = 2, Z = 1$):
$r = a_0 \dfrac{2^2}{1} = 4 a_0$

(B) For the $3^{\text{rd}}$ orbit of He$^+$ ($n = 3, Z = 2$):
$r = a_0 \dfrac{3^2}{2} = 4.5 a_0$

(C) For the $3^{\text{rd}}$ orbit of Li$^{2+}$ ($n = 3, Z = 3$):
$r = a_0 \dfrac{3^2}{3} = 3 a_0$

(D) For the $2^{\text{nd}}$ orbit of Be$^{3+}$ ($n = 2, Z = 4$):
$r = a_0 \dfrac{2^2}{4} = 1 a_0$

Therefore, the correct matching is (A)-(III), (B)-(IV), (C)-(II), (D)-(I).

Answer: (A)-(III), (B)-(IV), (C)-(II), (D)-(I)