To determine the correct increasing order of first ionization enthalpy for the second period elements, we need to understand the general trends and exceptions in ionization energies.$\\$The elements in the second period are:$\\$• Lithium (Li)$\\$• Beryllium (Be)$\\$• Boron (B)$\\$• Carbon (C)$\\$• Nitrogen (N)$\\$• Oxygen (O)$\\$• Fluorine (F)$\\$• Neon (Ne)$\\$The general trend is that ionization energy increases across a period from left to right due to increasing nuclear charge, which attracts the electrons more strongly. However, there are some exceptions to this trend:$\\$1. Beryllium (Be) has a higher ionization energy than Boron (B) because Be has a filled $s$ subshell, which is more stable.$\\$2. Nitrogen (N) has a higher ionization energy than Oxygen (O) because N has a half-filled $p$ subshell, which is more stable.$\\$Considering these points, the correct order of increasing first ionization enthalpy is:$\\$Li < B < Be < C < O < N < F < Ne$\\$This corresponds to Option 2.