The Bohr radius of a hydrogen-like species is | vedclass

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(D) The formula for the Bohr radius of a hydrogen-like species is given by $r_n = a_0 	imes \frac{n^2}{Z}$,where $a_0 = 52.9 	ext{ pm}$ is the Bohr

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$Li^{2+}, 2$

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(D) The formula for the Bohr radius of a hydrogen-like species is given by $r_n = a_0 	imes \frac{n^2}{Z}$,where $a_0 = 52.9 	ext{ pm}$ is the Bohr radius of the hydrogen atom,$n$ is the principal quantum number,and $Z$ is the atomic number.Given $r_n = 70.53 	ext{ pm}$,we have $70.53 = 52.9 	imes \frac{n^2}{Z}$.Calculating the ratio: $\frac{n^2}{Z} = \frac{70.53}{52.9} = 1.333... = \frac{4}{3}$.Testing the options:For option $D$: $Li^{2+}$ has $Z = 3$. If $n = 2$,then $\frac{n^2}{Z} = \frac{2^2}{3} = \frac{4}{3}$.This matches the calculated ratio. Therefore,the species is $Li^{2+}$ and the stationary state is $n = 2$.

The Bohr radius of a hydrogen-like species is $70.53 \text{ pm}$. The species and the stationary state $(n)$ are respectively (Given: Hydrogen atom Bohr radius is $52.9 \text{ pm}$)

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