Question

Which element has the highest second ionization energy: Li, \(\mathrm{K},\) or Be?

Short answer

Beryllium (Be) has the highest second ionization energy among Li, K, and Be due to its higher nuclear charge and proximity of the second electron to the nucleus, making it more difficult to remove.

Step-by-step solution

Recall the definition of ionization energy

Ionization energy is defined as the energy required to remove an electron from an atom or ion in its gaseous state. The second ionization energy refers specifically to the energy required to remove the second electron from an atom or ion.

Recall the factors affecting ionization energy

Ionization energy generally depends on three factors: 1. Atomic size (distance between the electrons and the nucleus) 2. Nuclear charge (number of protons in the nucleus) 3. Electron shielding (some electrons shield others from the attractive force of the nucleus)

Write the electronic configuration of the given elements

Write the electronic configuration of Li, K, and Be to better visualize their atomic structure. Lithium (Li): \( 1s^2 \ 2s^1 \) Potassium (K): \( 1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^1 \) Beryllium (Be): \( 1s^2 \ 2s^2 \)

Analyze the second ionization energy of the given elements

Now, consider the factors affecting ionization energy for the given elements during the process of losing the second electron. 1. Lithium (Li), after losing its first electron, will form a +1 ion with an electronic configuration of \( 1s^2 \). The next electron to be removed comes from the 1s orbital, which is closer to the nucleus and thus has a high ionization energy. 2. Potassium (K), after losing its first electron, will form a +1 ion with an electronic configuration of \( 1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \). The next electron to be removed is from the 3p orbital, which is further from the nucleus and thus has a lower ionization energy than Li. 3. Beryllium (Be), after losing its first electron, will form a +1 ion with an electronic configuration of \( 1s^2 \ 2s^1 \). The next electron to be removed comes from the 2s orbital, which is also closer to the nucleus and has a higher ionization energy than K. However, Be has a higher nuclear charge than Li, resulting in a stronger attraction between the nucleus and the remaining electron, which increases the ionization energy.

Identify the element with the highest second ionization energy

Comparing the factors affecting the second ionization energy for Li, K, and Be, we find that Beryllium (Be) has the highest second ionization energy due to its higher nuclear charge and proximity of the second electron to the nucleus, making it difficult to remove.

Key concepts

Atomic Size

Atomic size refers to the average distance from the nucleus of an atom to the outermost electrons. It plays a significant role in determining ionization energy. Smaller atomic size means that the outer electrons are closer to the nucleus. This results in a stronger attraction between the electrons and the nucleus, making it more difficult to remove an electron.

For the given elements—Lithium (Li), Potassium (K), and Beryllium (Be)—the atomic sizes vary:

• Lithium has a smaller atomic size compared to Potassium.
• Beryllium's atomic size is even smaller than Lithium's.

As a result, Beryllium's electrons feel a stronger pull from the nucleus, contributing to its high ionization energy. Atomic size helps explain why the removal of a second electron from Potassium is easier than from Beryllium or Lithium.

Nuclear Charge

Nuclear charge is the total charge within the nucleus, determined by the number of protons. This charge influences the attraction between the nucleus and electrons. Higher nuclear charge often leads to a stronger attraction, which increases ionization energy.

In comparing Li, K, and Be:

• Potassium has the highest nuclear charge because it has more protons than both Lithium and Beryllium.
• Beryllium, despite having a lower number of protons compared to Potassium, is unique. Its electrons are closer to the nucleus, allowing its nuclear charge to have a stronger effect on them compared to Lithium.

The high nuclear charge of Beryllium, therefore, contributes significantly to its high second ionization energy.

Electron Shielding

Electron shielding occurs when inner electrons block the outer electrons from the full attractive force of the nuclear charge. This effect reduces the effective nuclear charge felt by the outermost electrons, making them easier to remove.

In this context:

• Lithium has minimal shielding because it has fewer inner electron shells compared to Potassium.
• Beryllium's electron shielding is similar to Lithium's, with its inner electrons providing little shield to the outer electrons.

In Potassium, the multiple electron shells significantly shield the outermost 4s electron, decreasing its effective nuclear charge. This explains why Potassium has a lower second ionization energy relative to Beryllium. Beryllium's lack of extensive electron shielding means its outer electrons feel the nucleus's pull more acutely, resulting in higher ionization energy.