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

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.

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 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): \( 1s^2 \ 2s^2 \)

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.

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.