The radius of the first Bohr orbit of the hyd | vedclass

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(C) The radius of the $n^{	ext{th}}$ orbit of a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \mathring{A}$.For th

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$(2)$,$Be^{3+}$

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(C) The radius of the $n^{	ext{th}}$ orbit of a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \mathring{A}$.For the first orbit of the hydrogen atom $(n=1, Z=1)$,the radius is $r_1 = 0.529 \mathring{A}$.For the radius of the $n^{	ext{th}}$ orbit of species $X$ to be equal to the first Bohr orbit of hydrogen,we set $r_n = r_1$,which implies $\frac{n^2}{Z} = 1$,or $n^2 = Z$.Testing the options:For $Be^{3+}$,the atomic number $Z = 4$. Substituting $Z=4$ into $n^2 = Z$,we get $n^2 = 4$,which gives $n = 2$.Thus,for $n = 2$ and $X = Be^{3+}$,the condition is satisfied.

The radius of the first Bohr orbit of the hydrogen atom is the same as that of the orbit $(n)$ of a hydrogen-like species $X$. The values of $(n)$ and $X$ respectively are:

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