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 = -2.18 	imes 10^{-18} \ J 	imes \frac{Z

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 $E_n = -2.18 	imes 10^{-18} \ J 	imes \frac{Z^2}{n^2}$.For the first orbit $(n=1)$,the energy is directly proportional to the square of the atomic number $(Z^2)$.$\frac{E_H}{E_{He^{+}}} = \frac{Z_H^2}{Z_{He^{+}}^2}$Given $Z_H = 1$ and $Z_{He^{+}} = 2$,we have:$E_H = \frac{1^2}{2^2} 	imes E_{He^{+}}$$E_H = \frac{1}{4} 	imes (-871.6 	imes 10^{-20} \ J)$$E_H = -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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