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(D) The radius of the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $r_n = a_0 \frac{n^2}{Z}$,where $a_0$ is the Bohr radius,$n$ is t

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Doubly ionized lithium

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(D) The radius of the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $r_n = a_0 \frac{n^2}{Z}$,where $a_0$ is the Bohr radius,$n$ is the principal quantum number,and $Z$ is the atomic number.For the first orbit,$n = 1$,so $r_1 \propto \frac{1}{Z}$.Comparing the atomic numbers $(Z)$ for the given systems:- Hydrogen atom $(H)$: $Z = 1$- Deuterium atom $(D)$: $Z = 1$- Single ionized helium $(He^+)$: $Z = 2$- Doubly ionized lithium $(Li^{2+})$: $Z = 3$Since the radius $r$ is inversely proportional to $Z$,the system with the highest atomic number will have the minimum radius.Therefore,doubly ionized lithium $(Z = 3)$ has the minimum radius.

In which of the following systems will the radius of the first orbit $(n = 1)$ be minimum?

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