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Ch.8 - Periodic Properties of the Elements
Chapter 8, Problem 60

In Section 3.6, we estimated the effective nuclear charge on beryllium's valence electrons to be slightly greater than 2+. What would a similar treatment predict for the effective nuclear charge on boron's valence electrons? Would you expect the effective nuclear charge to be different for boron's 2s electrons compared to its 2p electron? In what way? (Hint: Consider the shape of the 2p orbital compared to that of the 2s orbital.)

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Effective Nuclear Charge (Z_eff)

Effective nuclear charge (Z_eff) refers to the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge (the number of protons) minus the shielding effect of inner-shell electrons. For beryllium and boron, Z_eff helps predict how strongly the valence electrons are attracted to the nucleus, influencing their chemical properties.
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Electron Shielding

Electron shielding occurs when inner-shell electrons repel outer-shell electrons, reducing the effective nuclear charge felt by the outer electrons. This phenomenon is crucial in understanding why valence electrons in different elements experience varying levels of attraction to the nucleus, affecting their reactivity and ionization energy.
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Orbital Shapes and Energy Levels

The shapes of atomic orbitals, such as 2s and 2p, influence the distribution of electrons around the nucleus. The 2s orbital is spherical, allowing it to be closer to the nucleus, while the 2p orbitals have a dumbbell shape, which can lead to different shielding effects. This difference in shape affects the effective nuclear charge experienced by electrons in these orbitals, with 2s electrons generally experiencing a higher Z_eff than 2p electrons.
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