Match List-I with List-II regarding the radius of Bohr orbits for...

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

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

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

(C) For the $1^{\text{st}}$ orbit of $\text{He}^{+}$ ($n = 1, Z = 2$):
$r = a_0 \dfrac{1^2}{2} = \dfrac{a_0}{2}$

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

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

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