The total energy of the electron of H^{-} ato | vedclass

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(D) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$. For the $H^{-}$ ion,which

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$-\frac{16}{9} E_2$

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(D) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$. For the $H^{-}$ ion,which is a two-electron system,the effective nuclear charge is not simply $Z=1$. However,in the context of standard textbook problems of this type,it is assumed to follow the Bohr model logic for hydrogen-like species. Given for $H^{-}$ $(Z=1)$ in the second quantum state $(n=2)$: $E_{H^-} = -k 	imes \frac{1^2}{2^2} = -\frac{k}{4} = -E_2$,which implies $k = 4E_2$. For the $He^{+}$ ion $(Z=2)$ in the third quantum state $(n=3)$: $E_{He^+} = -k 	imes \frac{2^2}{3^2} = -k 	imes \frac{4}{9}$. Substituting $k = 4E_2$: $E_{He^+} = -(4E_2) 	imes \frac{4}{9} = -\frac{16}{9} E_2$.

The total energy of the electron of $H^{-}$ atom in the second quantum state is $-E_2$. The total energy of the $He^{+}$ atom in the third quantum state is

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