The energy of the second orbit of a hydrogen | vedclass

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Question

(B) The energy of an orbit in a hydrogen-like species is given by the formula $E_n = -E_0 	imes \frac{Z^2}{n^2}$, where $E_0$ is the ground state ene

Vedclass · Accepted Answer

$-1.962 	imes 10^{-17}$

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(B) The energy of an orbit in a hydrogen-like species is given by the formula $E_n = -E_0 	imes \frac{Z^2}{n^2}$, where $E_0$ is the ground state energy of hydrogen $(2.18 	imes 10^{-18} \ J)$. For the second orbit of hydrogen $(n=2, Z=1)$: $E_2 = -2.18 	imes 10^{-18} 	imes \frac{1^2}{2^2} = -5.45 	imes 10^{-19} \ J$. For the first orbit of $Li^{2+}$ ion $(n=1, Z=3)$: $E_1 = -2.18 	imes 10^{-18} 	imes \frac{3^2}{1^2} \ J$ $E_1 = -2.18 	imes 10^{-18} 	imes 9 \ J$ $E_1 = -1.962 	imes 10^{-17} \ J$.

The energy of the second orbit of a hydrogen atom is $-5.45 \times 10^{-19} \ J$. What is the energy of the first orbit of $Li^{2+}$ ion (in $J$)?

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