1. Tardigrade
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  3. Physics
  4. N text th level of Li 2+ has the same energy as the ground state energy of the hydrogen atom. If rN and r1 be the radius of the N text th Bohr orbit of Li 2+ and first orbit radius of H atom, respectively, then the ratio (rN/r1) is

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Q. $N^{\text {th }}$ level of $Li ^{2+}$ has the same energy as the ground state energy of the hydrogen atom. If $r_{N}$ and $r_{1}$ be the radius of the $N^{\text {th }}$ Bohr orbit of $Li ^{2+}$ and first orbit radius of $H$ atom, respectively, then the ratio $\frac{r_{N}}{r_{1}}$ is

Atoms

Solution:

$E=\frac{E_{0} Z^{2}}{n^{2}}=E_{0} $
$\Rightarrow n=Z=3$
For Lithium, $r=\frac{r_{0} n^{2}}{Z}=\frac{r_{0} \cdot 3^{2}}{3}=3 r_{0}$