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  4. The radius of the first Bohr orbit of the H atom is r. Then, the radius of the first orbit of Li 2+ will be

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Q. The radius of the first Bohr orbit of the $H$ atom is $r$. Then, the radius of the first orbit of $Li ^{2+}$ will be

AMUAMU 2009

Solution:

Formula for radius of H-like species,
$r_{n}=0.529 \times \frac{n^{2}}{Z} \,\mathring{A}$
where, $0.529 \,\mathring{A}$ is the Bohr radius of H-atom
$n=$ principle quantum number,
$Z=$ atomic number
So, $r_{n}=\frac{r}{3}\left(\because n=1, Z=3\right.$ for $\left.Li ^{2+}\right)$