1. Resolving power
R = 500/0.25 = 2000.
| Criterion | Points |
|---|---|
| Correct setup | 5 |
| Correct R | 10 |
Worked Solutions
2. Radial velocity from one line
Δλ = 589.62−588.99 = 0.63 nm. v = (0.63/588.99)×299792 = 320.7 km/s (recession).
| Criterion | Points |
|---|---|
| Correct Δλ | 5 |
| Correct velocity | 10 |
3. Multi-line consistency
D2: Δλ = 0.63 nm, v = 320.3 km/s. Mean = 320.5 km/s; the two lines differ by only 0.2 km/s, well within expected measurement scatter, so they support a single bulk radial velocity.
| Criterion | Points |
|---|---|
| Correct D2 velocity | 8 |
| Correct consistency judgment | 7 |
4. Resolution versus shift
Resolution element = 500/2000 = 0.250 nm. The measured shift (0.63 nm) is about 2.5× the resolution element, so it is clearly resolved, not merely comparable to the instrumental limit.
| Criterion | Points |
|---|---|
| Correct resolution element | 8 |
| Correct comparison and judgment | 7 |
Grading Notes
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Common partial-credit errors: omitting units, failing to combine uncertainties in quadrature, or overstating the confidence of a marginal (SNR 3–5) result.