1. SNR classification
Noise term = 16 × (200 + 6 + 49) = 4080. SNR = 650/√(650+4080) = 9.45 — a secure detection (SNR > 5).
| Criterion | Points |
|---|---|
| Noise term | 5 |
| SNR value | 5 |
| Classification | 5 |
Worked Solutions
2. Zero-point application
Rate = 95000/30 = 3166.7 counts/s. m = −2.5×log10(3166.7) + 19.457 = -8.752 + 19.457 = 10.706.
| Criterion | Points |
|---|---|
| Rate computed | 5 |
| Correct magnitude | 10 |
3. Aperture bias
Δm = −2.5×log10(1/0.80) = -0.242 mag. Because only part of the flux is captured, the measured magnitude is too faint (fainter) by 0.242 mag relative to the true value.
| Criterion | Points |
|---|---|
| Correct sign and magnitude | 10 |
| Correct interpretation | 5 |
4. Uncertainty budget
σ_total = √(0.02² + 0.018²) = 0.027 mag. Report: m = 10.71 ± 0.03.
| Criterion | Points |
|---|---|
| Quadrature method | 8 |
| Correctly combined final report | 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.