The energy of the second Bohr orbit of the hy | vedclass

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

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$-3.4$

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(A) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$. For the hydrogen atom $(Z=1)$,the energy of the second orbit $(n=2)$ is $E_2 = -13.6 	imes \frac{1^2}{2^2} = -3.4 \ eV$. For the $He^{+}$ ion,the atomic number $Z=2$. We need to find the energy of the fourth orbit $(n=4)$. Substituting these values into the formula: $E_4 = -13.6 	imes \frac{2^2}{4^2} \ eV$. $E_4 = -13.6 	imes \frac{4}{16} \ eV$. $E_4 = -13.6 	imes \frac{1}{4} \ eV$. $E_4 = -3.4 \ eV$.

The energy of the second Bohr orbit of the hydrogen atom is $-3.4 \ eV$. The energy of the fourth Bohr orbit of the $He^{+}$ ion will be: (in $eV$)

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