To solve this problem, we need to understand the concept of first ionization enthalpy.$\\$First ionization enthalpy is the energy required to remove the outermost electron from a neutral atom in the gaseous state.$\\$The general trend in the periodic table is that ionization enthalpy increases across a period from left to right$\\$due to increasing nuclear charge and decreases down a group due to increasing atomic size.$\\$Let's analyze the given elements: Li, Be, B, C, N. All these elements belong to the second period of the periodic table.$\\$• Li (Lithium) is in Group 1.$\\$• Be (Beryllium) is in Group 2.$\\$• B (Boron) is in Group 13.$\\$• C (Carbon) is in Group 14.$\\$• N (Nitrogen) is in Group 15.$\\$The expected order of increasing ionization enthalpy across a period is:$\\$Li < Be < B < C < N.$\\$However, there are some exceptions to this trend due to electronic configuration stability.$\\$Beryllium (Be) has a filled s-subshell, which makes it more stable and gives it a higher ionization enthalpy than Boron (B).$\\$Therefore, the correct order considering this exception is:$\\$Li < B < Be < C < N.$\\$This corresponds to Option 4.