Estimate the effective nuclear charge felt by the 3s electron in the sodium atom, if the ionization energy is 5.14 eV. Select one: a. 1.84 b. 11 c. 2.12 d. 5.7
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It is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner electrons. Show more…
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The measured energy of a 3s state of sodium is -5.138 eV. Calculate the value of Zeff.
Sri K.
If the $3 s$ electron in sodium did not penetrate the inner core, its energy would be $-13.6 \mathrm{eV} / 3^{2}=-1.51 \mathrm{eV} .$ Because it does penetrate, it sees a higher effective $Z$ and its energy is lower. Use the measured ionization potential of $5.14 \mathrm{~V}$ to calculate $Z_{\text {eff }}$ for the $3 s$ electron in sodium.
If the outer electron in lithium moves in the $n=2$ Bohr orbit, the effective nuclear charge would be $Z_{\text {eff }} e=1 e,$ and the energy of the electron would be $-13.6 \mathrm{eV} / 2^{2}=-3.4 \mathrm{eV}$. However, the ionization energy of lithium is $5.39 \mathrm{eV},$ not $3.4 \mathrm{eV}$ Use this fact to calculate the effective nuclear charge $Z_{\text {eff }}$ seen by the outer electron in lithium. Assume that $r=4 a_{0}$ for the outer electron.
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