- #31
Vuldoraq
- 265
- 1
Looks good to me. 
Radioactive Decay Differential Equation Question
- Thread starter TFM
- Start date
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Homework Help Overview
The discussion revolves around a problem involving the radioactive decay of a fictional element called Unobtainium, described by the differential equation u' = −k u. The half-life of Unobtainium is given as 2.3 × 10^9 years, with participants attempting to find the decay constant k and the number of decay events per second in a 1 kg block of the element.
Discussion Character
- Exploratory, Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants explore the relationship between the half-life and the decay constant k, with attempts to derive k from the equation and the half-life. Questions arise about the integration constants and the setup of the equations. There is also discussion on how to calculate the number of decay events based on the atomic mass and the total mass of Unobtainium.
Discussion Status
The discussion has progressed with participants providing insights into the calculations for k and the number of decay events. Some have offered guidance on converting units and clarifying the relationship between the number of atoms and decay events. Multiple interpretations of the calculations are being explored, particularly regarding the conversion of k to per second.
Contextual Notes
Participants note the need to consider the atomic mass of Unobtainium and its implications for calculating the number of atoms in a 1 kg sample. There is also mention of the need to convert the decay constant from years to seconds for accurate calculations.
- #32
TFM
- 1,016
- 0
Execellent.
Thanks for your assitance, Vuldoraq and Tiny-Tim
TFM
Thanks for your assitance, Vuldoraq and Tiny-Tim
TFM
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