Questions: Computational studies have determined the effective nuclear charge, Zeff, for an electron in a particular 5^5 subshell to a high degree of certainty. The table lists the calculated Zeff values for a 1s, 2s, and 2p orbital of boron. From the provided values of effective nuclear charge, estimate the energy, εn, of a 1s, 2s, and 2p orbital of boron. A rydberg (Ry) is a unit of energy approximately equal to 13.6 eV. B Zeff 1s 4.68 2s 2.58 2p 2.42 In terms of the Bohr radius, a0, estimate the average distance of the electron from the nucleus, r̄(n, ℓ), for an electron in a 1s, 2s, and 2p orbital of boron. r̄(1,0)= square a0 r̄(2,0)= square a0 1s= -21.9024 2s=-1.6647 2p= -1.4641
Transcript text: Computational studies have determined the effective nuclear charge, $Z_{\text {eff }}$, for an electron in a particular ${ }_{5}^{5}$ subshell to a high degree of certainty. The table lists the calculated $Z_{\text {eff }}$ values for a $1 s, 2 s$, and $2 p$ orbital of boron.
From the provided values of effective nuclear charge, estimate the energy, $\epsilon_{n}$, of a $1 s, 2 s$, and $2 p$ orbital of boron. A rydberg (Ry) is a unit of energy approximately equal to 13.6 eV .
\begin{tabular}{|c|c|}
\hline B & $Z_{\text {eff }}$ \\
\hline $1 s$ & 4.68 \\
\hline $2 s$ & 2.58 \\
\hline $2 p$ & 2.42 \\
\hline
\end{tabular}
In terms of the Bohr radius, $a_{0}$, estimate the average distance of the electron from the nucleus, $\bar{r}_{n, \ell}$, for an electron in a $1 s, 2 s$, and $2 p$ orbital of boron.
\[
\begin{array}{l}
\bar{r}_{1,0}=\square a_{0} \\
\bar{r}_{2,0}=\square a_{0}
\end{array}
\]
\[
\begin{array}{l}
1 s= \\
-21.9024 \\
2 s=-1.6647 \\
2 p= \\
-1.4641
\end{array}
\]
Solution
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