The energy of the electron in the first orbit | vedclass

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(C) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$ or $

Vedclass · Accepted Answer

$-217.9 	imes 10^{-20} \ J$

Vedclass · Answer

(C) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$ or $E_n \propto Z^2$. For the first orbit $(n=1)$,$E_1 \propto Z^2$. Given for $He^{+}$ $(Z=2)$: $E_{1, He^{+}} = -871.6 	imes 10^{-20} \ J$. For Hydrogen $(Z=1)$: $E_{1, H} = E_{1, He^{+}} 	imes \frac{Z_H^2}{Z_{He^{+}}^2}$. $E_{1, H} = -871.6 	imes 10^{-20} 	imes \frac{1^2}{2^2} = -871.6 	imes 10^{-20} 	imes \frac{1}{4} = -217.9 	imes 10^{-20} \ J$.

The energy of the electron in the first orbit of $He^{+}$ is $-871.6 \times 10^{-20} \ J$. The energy of the electron in the first orbit of hydrogen would be

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