Fundamental units: Which of the following is not a unit of length in science and engineering usage?

Introduction / Context:
Recognising physical units and their dimensions prevents serious calculation errors. While many specialised units exist for length at astronomical or subatomic scales, some similarly named units measure different physical quantities entirely.

Given Data / Assumptions:

• We compare common physics units across astronomy and nuclear/atomic physics.
• We focus on dimensionality: length versus area.

Concept / Approach:
Parsec (pc), Angstrom (Å), and Fermi (fm) are all units of length. In contrast, a Barn (b) is a unit of area used for nuclear cross-sections, equal to 10^-28 m^2, not a length.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional analysis confirms Barn has dimension L^2, unlike the others (dimension L).

Why Other Options Are Wrong:

• Parsec, Angstrom, Fermi: All are indeed length units across different scales.

Common Pitfalls:
Assuming similarity by name (“Fermi” vs “Fermion”) or scale; always verify dimensionality to avoid mixing units such as area, volume, or energy with length.

Final Answer:
Barn