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Chemistry Question on Structure of atom

The radius of hydrogen atom in the ground state is 0.53 A˚.\mathring{A}. The radius of Li2+Li^{2+} ion (at. no. = 3) in a similar state is

A

0.17A˚0.17 \mathring{A}

B

0.53A˚0.53 \mathring{A}

C

0.265A˚0.265 \mathring{A}

D

1.06A˚1.06 \mathring{A}

Answer

0.17A˚0.17 \mathring{A}

Explanation

Solution

We know that rnr_n (H-like)=rn(H−atom)×n2Z=\frac{r_n (H - atom)\times n^2}{Z}
For ground state, n = 1
∴         rn(Li2+)=053A˚×(1)23\therefore\, \, \, \, \, \, \, \, \, r_n(Li^{2+})=\frac{053 \mathring{A} \times (1)^2}{3}
(Li,Z=3)=0.17A˚(Li,Z = 3) = 0.17\mathring{A}