Apply Bohr's atomic model to a lithium atom. | vedclass

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(B) In a lithium atom $(Z=3)$,there are $3$ electrons. Two electrons are in the $K$-shell $(n=1)$.According to the problem,these two electrons screen

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$3.4$

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(B) In a lithium atom $(Z=3)$,there are $3$ electrons. Two electrons are in the $K$-shell $(n=1)$.According to the problem,these two electrons screen the nucleus such that the effective charge seen by the outermost electron is $Z_{eff} = 3 - 2 = 1$.The outermost electron is in the $L$-shell $(n=2)$.The energy of an electron in a hydrogen-like atom is given by $E_n = -13.6 	imes \frac{Z_{eff}^2}{n^2} 	ext{ eV}$.For the outermost electron,$n=2$ and $Z_{eff}=1$.$E_2 = -13.6 	imes \frac{1^2}{2^2} = -13.6 	imes \frac{1}{4} = -3.4 	ext{ eV}$.The ionization energy is the energy required to remove the electron from $n=2$ to $n=\infty$,which is $E_{\infty} - E_2 = 0 - (-3.4) = 3.4 	ext{ eV}$.

Apply Bohr's atomic model to a lithium atom. Assuming that its two $K$-shell electrons are so close to the nucleus that the nucleus and the $K$-shell electrons act as a core with an effective positive charge equivalent to $1e$. The ionization energy of its outermost electron is......$eV$.

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