Step 1: Understanding ionization energies.
Ionization energy increases across a period and decreases down a group. However, there are exceptions due to electron configurations, especially in p-block elements.
Step 2: Explanation of the order.
- Li (Lithium) has the lowest first ionization energy because it is an alkali metal with a single electron in its outermost shell.
- Be (Beryllium) has a higher ionization energy than Li because it has a stable \( 2s^2 \) configuration.
- B (Boron) has a lower ionization energy than C because it has one electron in the \( 2p \) orbital, which is easier to remove than a fully filled \( 2s^2 \) orbital in carbon.
- C (Carbon) has the highest first ionization energy because it has a half-filled \( 2p^2 \) orbital, which is relatively stable.
Step 3: Conclusion.
Thus, the correct order of increasing first ionization energy is:
\[
\text{Li}<\text{Be}<\text{B}<\text{C}
\]
which corresponds to option (D).