Step 1: Ionization Energy Trends
The ionization energy is the energy required to remove an electron from an atom.
Ionization energies generally increase across a period from left to right in the periodic table.
However, there are some exceptions due to the electron configurations of the elements.
Step 2: Explanation of the Trend for the Given Elements
\( Be \) has the lowest ionization energy because its electron configuration is stable with a fully filled \( 2s \) orbital.
\( B \) has a slightly lower ionization energy than \( C \) because removing an electron from a \( 2p \) orbital in \( B \) is easier than removing one from a more stable \( 2s \) orbital in \( C \).
\( O \) has a higher ionization energy than \( N \) because oxygen has paired electrons in its \( 2p \) orbitals, which experience repulsion, making it easier to ionize.
Step 3: Conclusion
Thus, the correct order is \( \text{Be} < \text{B} < \text{C} < \text{O} < \text{N} \).