One gram of cadmium contains (.1222/113)(6.02E23) = 6.5E20 atoms of
Cd-113. A half-life of 7.7E15 years corresponds to a decay constant of (ln
2) / (7.7E15) = 9E-17 per year. Conclusion: each gram of Cd will
experience 58600 (+/- 250 or so ... a perfect example of a Poisson
distributed random variable in nature!) beta decays per year, or an
average "time between clicks" of 9 minutes.
How much Cd is in a cellphone battery? That I don't know. Typical NiCd
battery is 18% Cd by weight; I don't have a cell phone, so taking the
battery out of your phone, weighing it, and doing the mulitiplication is
left as an exercise to the reader.
Curious coincidence: 77x9=693. Sheer speculation: it's the decay constant,
not the half-life, that you can actually experimentally measure, for a
long-lived nuclide. Do you suppose they actually measured the rate to be
9.0E-17, or was it something they could only determine to one significant
figure?
Gordon Bower
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beta decay (e-)
Assume 50 grams of Cd, there 6.11 grams of Cd-113
6.11 gm/2 = 3.055 gm in 7.7*10^15
3.055 gram is 3.055/113 -6.02*10^23 = 1.628*10^22 Cd Atoms
1.628*10^22 / 7.7*10^15 yr yr/365.25 day day/ 24 hr = .067 Hz
0.067 Hz * 3600 = 241 ... about 240 clicks per hour
Matt Coury
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