Which of the following statements are correct | vedclass

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(B) $I$) The energy of the hydrogen atom in its ground state $(n=1)$ is given by $E_n = -13.6 \ eV / n^2$. For $n=1$,$E_1 = -13.6 \ eV$. Thus,statemen

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$I$ & $III$ only

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(B) $I$) The energy of the hydrogen atom in its ground state $(n=1)$ is given by $E_n = -13.6 \ eV / n^2$. For $n=1$,$E_1 = -13.6 \ eV$. Thus,statement $I$ is correct.$II$) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by $r_n = 52.9 	imes n^2 / Z \ pm$. For $H$ $(Z=1)$ and $n=3$,$r_3 = 52.9 	imes 3^2 / 1 = 476.1 \ pm$. Thus,statement $II$ is incorrect.$III$) The radius of the first orbit $(n=1)$ is $r_1 = 52.9 	imes (1^2 / Z) \ pm$. As $Z$ increases,$r_1$ decreases. The atomic numbers are $H(1), He^{+}(2), Li^{2+}(3), Be^{3+}(4)$. Therefore,the order of radii is $H > He^{+} > Li^{2+} > Be^{3+}$. Thus,statement $III$ is correct.Conclusion: $I$ and $III$ are correct.

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