Step 1: Ionization energy trend.
Ionization energy increases across a period (from left to right) because the atomic size decreases, leading to a stronger attraction between the nucleus and the electrons. Ionization energy decreases down a group because the outermost electrons are farther from the nucleus and more shielded by inner electrons.
Step 2: Analyze the elements.
- Lithium (Li) has the lowest ionization energy because it is in Group 1.
- Boron (B) has a higher ionization energy than Li but less than Be and C.
- Beryllium (Be) has a higher ionization energy due to its stable \(s^2\) electron configuration.
- Carbon (C) has the highest ionization energy because it is farther across the period and has a relatively small atomic size.
Step 3: Conclusion.
The order of increasing first ionization energy is:
\[
\text{Li}<\text{B}<\text{Be}<\text{C}
\]
Final Answer:
\[
\boxed{\text{(C), (B), (A), (D)}}
\]