Activity, Sample Size, Dating, and Tracers
Activity A = lambda N is measured in becquerels, where 1 Bq = 1 s^-1; 1 Ci = 3.7 x 10^10 Bq. N can be related to sample mass through N = (m/M)N_A, subject to detector efficiency when measured counts are used.
Why this shows up in the exam
Radioisotope dating · Medical tracer dilution · Finding sample mass from activity
Learn the idea
Activity equals lambda times the number of radioactive nuclei, linking count rate to sample amount and age. A sample is more active if it contains more radioactive nuclei or if each nucleus has a larger decay probability per second. Measuring activity can therefore reveal amount, elapsed time, or tracer dilution.
🧠 Memory hook: Activity is lambda times how many radioactive nuclei remain.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- A = lambda N — decays per second for N nuclei with decay constant lambda
- N = (m/M) N_A — radioactive nuclei in a pure sample of mass m and molar mass M
- A/A0 = e^(-lambda t) — age relation when initial and present activities are comparable
How to approach it
- 1Convert half-life to lambda
- 2Relate N to moles when mass is given
- 3Apply decay during any delay before using dilution data
Common slip-ups that cost marks
- •Equating detector counts with activity without efficiency assumptions
- •Using total sample mass when only a fraction is radioactive
- •Mixing curies and becquerels
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
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