# Assessment Instructions: Problem Set 02 — The 21 cm Line and HI Column Density

## Inputs to Inspect
Student submission, this problem set, the solution key, the corresponding lecture slides/notes, and the referenced dataset(s) under `materials/ASTR360/data/`.

## Grading Standard
Award credit for correct method and units first, then for the specific numeric result. A student who shows correct reasoning with a small arithmetic slip should receive most of the available credit; a student with a correct-looking number but no visible derivation steps should not. Because this is a 300-level quantitative interstellar-medium course, full marks require a genuine derivation wherever the problem set asks for one, and a genuinely reasoned (not merely asserted) interpretation wherever the problem asks for scientific judgment (e.g., honestly characterizing an idealized model's disagreement with a real object).

## Problem-Level Criteria
- Problem 1: verify correct exponential evaluation and a reasoned (not merely numeric) qualitative comparison.
- Problem 2: verify the Gaussian-integral coefficient (sqrt(pi/(4 ln2))) is included, not omitted.
- Problem 3: verify the Galactic-latitude reasoning is physically correct (lower latitude means more HI, not less).
- Problem 4: verify the direction of the optically thin approximation's error (over-estimate, not under-estimate) is stated correctly.

## Resubmission Policy
Students may resubmit within one week of receiving feedback. A resubmission must show a corrected derivation, not only a corrected final number, and should reference the specific feedback comment it addresses. Regrade to a maximum of 90% of the original point value unless the error was a grading mistake.

## Common Errors to Flag
- Omitting the sqrt(pi/(4 ln2)) ≈ 1.0645 Gaussian-integral factor entirely.
- Reversing which sightline (Cygnus X-1 vs 3C 273) has the higher column density.
- Stating the optically thin approximation always under-estimates N(HI) regardless of optical depth (it can go either direction depending on the specific formula being compared, but for this brightness-temperature comparison at tau=0.5 it over-estimates).