The radius of which of the following orbits i | vedclass

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(D) The radius of an orbit in a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.For the first Bohr or

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$Be^{3+}(n = 2)$

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(D) The radius of an orbit in a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.For the first Bohr orbit of the hydrogen atom $(H)$: $n = 1$ and $Z = 1$. Thus,$r_H = 0.529 	imes \frac{1^2}{1} = 0.529 \ \mathring{A}$.Now,checking the options:For $Be^{3+}$: $Z = 4$ and $n = 2$. Thus,$r = 0.529 	imes \frac{2^2}{4} = 0.529 	imes \frac{4}{4} = 0.529 \ \mathring{A}$.Since the radius of $Be^{3+}$ $(n = 2)$ is equal to the radius of the first Bohr orbit of hydrogen,the correct option is $D$.

The radius of which of the following orbits is the same as that of the first Bohr's orbit of the hydrogen atom?

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