Deriving Error Equations for Half-Life Calculations

AI Thread Summary
To derive the error equation for half-life calculations, start with the formula t1/2 = ln(2)/λ, where λ is the decay constant. The error in half-life can be expressed as σ(t1/2) = σ(ln2)/(ln2) + σ(λ)/λ. The derivation involves understanding the relationship between the number of remaining nuclei and time based on the initial quantity and decay rate. It is essential to clarify whether an error bound on the decay rate is assumed and if a normal distribution for the error in decay rate can be justified. This foundational understanding is crucial for accurately calculating the half-life and its associated errors.
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Homework Statement



How to derive an error equation: t1/ 2 = ln 2/λ= 0.693/λ. Confused, and don't even know where to start.

2. The attempt at a solution
σ(t1/2)= σ(ln2)/(ln2) + σ(λ)/λ
 
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Start by writing the equation for radioactive decay and derive the relation between number of nuclei remaining and time ( using initial number of nuclei and the rate constant as known quantities). Once you obtain the relation, set the number of remaining nuclei to half of the initial value and then solve for time taken.
 
Not sure I understand the question. Is it that you have an error bound on the decay rate, and you wish to derive from that an error bound for the half life? Are you assuming (and can you justify) a normal distribution for the error in the decay rate?
 

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