Atomic Structure And Electron Configuration

The nucleus contains protons and neutrons. The number of protons (atomic number) determines the identity of the element, because each element has a unique number of protons.

A neutral sodium atom has 11 protons and 11 electrons. When sodium loses one electron to form Na⁺, it has 11 protons but only 10 electrons, so the net charge is +1 because the positive charges outnumber the negative charges.

The force on the 1s electron is stronger. According to Coulomb’s law, force is inversely proportional to the square of the distance. The 1s electron is much closer to the nucleus than the 3s electron, so $r$ is smaller, resulting in a significantly larger attractive force.

Mg²⁺ has 12 protons while Na⁺ has 11 protons, so the nuclear charge (${q}_{1}$) is greater in Mg²⁺. Both ions have the same number of electrons and a similar electron configuration, so the distance and shielding are comparable. The greater nuclear charge in Mg²⁺ increases the magnitude of ${q}_{1}{q}_{2}/{r}^{2}$, producing a stronger attractive force on each electron.

According to Coulomb’s law, force is proportional to $1/{r}^{2}$. If the distance is doubled, ${r}^{2}$ increases by a factor of 4, so the electrostatic force decreases to one-quarter of its original value.

1s² 2s² 2p⁶ 3s² 3p⁴. Sulfur has 16 electrons. Following the Aufbau principle, the subshells fill in order: 1s (2), 2s (2), 2p (6), 3s (2), and the remaining 4 electrons enter the 3p subshell.

1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁹. Neutral copper has the configuration [Ar] 4s¹ 3d¹⁰ (an exception). To form Cu²⁺, remove 2 electrons starting from the highest energy level: first the one 4s electron, then one 3d electron, leaving 3d⁹.

Phosphorus (1s² 2s² 2p⁶ 3s² 3p³) has 5 valence electrons. Valence electrons occupy the outermost shell, which is $n$ = 3 for phosphorus. The 3s subshell holds 2 electrons and the 3p subshell holds 3 electrons, giving a total of 5 valence electrons.

Core electrons are in the inner, fully filled shells and are not involved in bonding. Valence electrons are in the outermost shell and participate in chemical reactions. In silicon (1s² 2s² 2p⁶ 3s² 3p²), the 10 electrons in $n$ = 1 and $n$ = 2 are core electrons, while the 4 electrons in $n$ = 3 (3s² 3p²) are valence electrons.

The first electron removed from sodium is a 3s valence electron, which is far from the nucleus and well shielded by 10 core electrons, resulting in low $Z_{\mathrm{eff}}$ and low ionization energy. The second electron must be removed from the 2p core shell, which is much closer to the nucleus and shielded by fewer electrons. According to Coulomb’s law, the smaller distance and higher effective nuclear charge produce a much stronger attractive force, so substantially more energy is required.

The first ionization energy of oxygen is less than that of nitrogen. Although oxygen has a higher nuclear charge, in the 2p subshell, nitrogen has a half-filled 2p³ configuration while oxygen has 2p⁴. The fourth 2p electron in oxygen must pair with another electron in the same orbital, and the resulting electron-electron repulsion partially offsets the increased nuclear attraction. This additional repulsion makes the electron easier to remove, decreasing oxygen’s first ionization energy relative to nitrogen’s.

Actual nuclear charge equals the total number of protons in the nucleus. Effective nuclear charge ($Z_{\mathrm{eff}}$) is the net positive charge felt by a particular electron after accounting for the shielding effect of inner (core) electrons. Core electrons repel outer electrons and partially cancel the attractive force of the nucleus. Because valence electrons are shielded by all the core electrons beneath them, they experience a $Z_{\mathrm{eff}}$ that is significantly less than the actual nuclear charge, which results in a weaker attractive force and lower ionization energy compared to core electrons.

Magnesium has a higher first ionization energy than aluminum. Magnesium’s outermost electron is in the 3s subshell, while aluminum’s outermost electron is in the 3p subshell. The 3p electron is, on average, slightly farther from the nucleus and is shielded by both the core electrons and the 3s² electrons beneath it. According to Coulomb’s law, the greater distance and increased shielding reduce the attractive force on aluminum’s 3p electron, making it easier to remove despite aluminum having one additional proton.