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  4. The radius of hydrogen atom in the ground state is 0.53 mathringA . The radius of Li 2+ ion (at. no. =3 ) in a similar state is

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

AIPMTAIPMT 1995Structure of Atom

Solution:

We know that $I_{n}( H$-like $)=\frac{r_{n}( H -\text { atom }) \times n^{2}}{Z}$
For ground state, $n=1$
$\therefore r_{n}\left( Li ^{2+}\right) =\frac{0.53 \,\mathring{A} \times(1)^{2}}{3} $
$( Li , Z=3) =0.17\,\mathring{A} $