Question

Which has the larger second ionization energy, lithium or beryllium? Why?

Short answer

Lithium has a larger second ionization energy compared to beryllium, due to the more stable electron configuration of the Li\(^+\) ion and the combined effects of effective nuclear charge and electron shielding.

Step-by-step solution

Write the electron configuration for lithium and beryllium

The electron configuration for lithium (atomic number 3) is \(1s^2 2s^1\), and the electron configuration for beryllium (atomic number 4) is \(1s^2 2s^2\).

Determine the electron configurations after the first ionization

After the first ionization, one electron is removed from each atom. The electron configuration for lithium will be \(1s^2\) (now Li\(^+\)) and for beryllium, it will be \(1s^2 2s^1\) (now Be\(^+\)).

Compare the remaining electron configurations

The remaining electron configuration for Li\(^+\) is a completely filled 1s orbital, and the electron configuration for Be\(^+\) includes a half-filled 2s orbital, which is more stable.

Determine the larger second ionization energy

Since it requires more energy to remove an electron from Li\(^+\) (with a completely filled 1s orbital) than from Be\(^+\) (with a half-filled 2s orbital), lithium has a larger second ionization energy.

Discuss the reason behind the difference in ionization energy

This difference can be explained by effective nuclear charge and electron shielding. When an electron is removed from the 2s orbital in Be, the remaining electron experiences a stronger attraction to the nucleus due to the removed electron's shielding effect being diminished. In the case of Li, removing an electron from the completely filled 1s orbital requires more energy because it is closer to the nucleus, more tightly bound, and the shielding effect of the core electrons is less effective in reducing the effective nuclear charge experienced by the valence electron.

Conclusion

Lithium has a larger second ionization energy compared to beryllium, due to the more stable electron configuration of the Li\(^+\) ion and the combined effects of effective nuclear charge and electron shielding.

Key concepts

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's electron shells and orbitals. Electrons occupy these energy levels based on the principle of minimizing energy. They fill orbitals starting from those with the lower energy to those with higher energy.

For lithium, which has an atomic number of 3, the electron configuration is written as \(1s^2 2s^1\). This means lithium has two electrons in the first energy level (1s orbital) and one electron in the second energy level (2s orbital).

• First energy level: Two electrons
• Second energy level: One electron

Beryllium, with an atomic number of 4, has the electron configuration \(1s^2 2s^2\). Beryllium's electrons are also arranged in the first and second orbitals.

• First energy level: Two electrons
• Second energy level: Two electrons

After the first ionization, the electron arrangement changes, like for lithium becoming \(1s^2\) and for beryllium changing to \(1s^2 2s^1\). Understanding these configurations helps determine their ionization energies.

Effective Nuclear Charge

Effective nuclear charge (\(Z_{eff}\)) is the net positive charge experienced by an electron in a multi-electron atom. The concept accounts for the shielding effect of core electrons which reduce the full nuclear charge felt by outer electrons.

An electron close to the nucleus has a higher effective nuclear charge because the inner electrons shield this attraction less effectively. In simpler terms, the electron feels a stronger pull from the protons in the nucleus. In lithium, after the first electron is removed, \(Z_{eff}\) experienced by the remaining 1s electron is significant because there's less shielding. This contributes to a higher second ionization energy as removing another electron becomes more difficult.

In beryllium, after the first ionization, there's less of an increase in \(Z_{eff}\) for its remaining s-electron (in \(2s^1\)), as they have one more electron left to shield them partially. This means it's relatively easier to remove another electron compared to lithium, which explains the difference in their second ionization energies.

Electron Shielding

Electron shielding occurs when inner-shell electrons partially block the nuclear charge, effectively reducing the electrostatic interactions between the nucleus and the valence electrons. This phenomenon is crucial when considering ionization energy, particularly the second ionization energy.

• In lithium, the remaining electron in the \(1s^2\) orbital after losing the outer electron, feels stronger nuclear attraction due to less electron shielding.
  
  
• In beryllium, even after the first electron is removed, a remaining electron in \(2s^1\) still benefits from some level of shielding from fellow core electrons.

This concept of electron shielding helps explain why lithium's second ionization energy is larger than beryllium, as Be still retains additional electron layers that contribute to shielding.

Atomic Structure

The atomic structure of an element is determined by the arrangement and energy levels of its electrons around the nucleus. This structure greatly influences physical and chemical properties, such as ionization energies.

In the case of lithium and beryllium, their atomic structures reveal vital information about their ionization energies. Lithium has a simple structure with three electrons, where its second ionization involves removing one of its stable 1s electrons. This requires significant energy due to the electron's proximity to the nucleus and minimal shielding.

• Lithium structure: Stable after losing its single valence electron.
• Beryllium structure: Less energy required to remove a second electron due to its \(2s^1\) configuration.

The atomic structure thus provides insights into how tightly the electrons are held, and how likely they are to be removed during successive ionizations. This directly influences chemical reactivity and bonding characteristics.