Bayesian parameter estimation for an undergraduate radioactive silver decay experiment

Abstract

At Carleton College an important undergraduate laboratory experiment involves the neutron activation of silver. Using a neutron howitzer, thermal neutrons are aimed at US quarter coins that were made before 1965, and hence contain 107 Ag and 109 Ag. These two isotopes occur naturally in almost equal proportions. After neutron activation 108 Ag and 110 Ag are created, which then decay with half-lives of 143 s and 24.6 s respectively. The students measure the decay rate, of both isotopes combined, with Geiger counters. Here we present a Bayesian Markov chain Monte Carlo method to estimate the half-lives of the two silver isotopes. We use real data to derive the half-lives, but we also use simulated data to highlight the features of the data analysis technique. This presentation is intended for undergraduate physics teachers such that they may introduce parameter estimation to their students in their laboratory based classes. The code has been made publicly available.

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BibTeX RIS

BibTeX

@article{meyer2026bayesian,
  title = {{Bayesian parameter estimation for an undergraduate radioactive silver decay experiment}},
  author = {Renate Meyer and Nelson Christensen and Jay Tasson},
  journal = {European Journal of Physics},
  year = {2026},
  month = oct,
  doi = {10.1088/1361-6404/aeb0e5},
  url = {https://hal.science/hal-05856347v1},
  note = {CC BY},
}

RIS

TY  - JOUR
TI  - Bayesian parameter estimation for an undergraduate radioactive silver decay experiment
AU  - Renate Meyer
AU  - Nelson Christensen
AU  - Jay Tasson
PY  - 2026
DA  - 2026/10/27
JO  - European Journal of Physics
DO  - 10.1088/1361-6404/aeb0e5
UR  - https://hal.science/hal-05856347v1
AB  - At Carleton College an important undergraduate laboratory experiment involves the neutron activation of silver. Using a neutron howitzer, thermal neutrons are aimed at US quarter coins that were made before 1965, and hence contain 107 Ag and 109 Ag. These two isotopes occur naturally in almost equal proportions. After neutron activation 108 Ag and 110 Ag are created, which then decay with half-lives of 143 s and 24.6 s respectively. The students measure the decay rate, of both isotopes combined, with Geiger counters. Here we present a Bayesian Markov chain Monte Carlo method to estimate the half-lives of the two silver isotopes. We use real data to derive the half-lives, but we also use simulated data to highlight the features of the data analysis technique. This presentation is intended for undergraduate physics teachers such that they may introduce parameter estimation to their students in their laboratory based classes. The code has been made publicly available.
SN  - 0143-0807
SN  - 1361-6404
ER  -

Abstract

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