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  4. The radius of hydrogen atom in the ground state is 0.53 mathringA . The radius of Li2+ ion (atomic number = 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 (atomic number $ = 3 $ ) in a similar state is :

UPSEEUPSEE 2005

Solution:

$r_{4}=\frac{r_{0} \times n^{2}}{Z}$

Given, $r_{0}=$ radius of $H$ atom in ground state $=0.5\, \mathring{A}$

$n=$ number of orbit $=1$

$Z=$ Atomic number of $Li =3$

$\therefore \, r_{4}=\frac{0.53 \times 1^{2}}{3}$

$=0.176\, \mathring{A}$