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

Question

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 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

E=(E0 Z2/n2)=E0 ⇒ n=Z=3 For Lithium, r=(r0 n2/Z)=(r0 ⋅ 32/3)=3 r0

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

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

Q. Nth level of Li2+ has the same energy as the ground state energy of the hydrogen atom. If rN​ and r1​ be the radius of the Nth Bohr orbit of Li2+ and first orbit radius of H atom, respectively, then the ratio r1​rN​​ is

E=n2E0​Z2​=E0​ ⇒n=Z=3 For Lithium, r=Zr0​n2​=3r0​⋅32​=3r0​

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

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