Deriving Error Equations for Half-Life Calculations

[dab353]

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

 

[Sunil Simha]

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.

 

[haruspex]

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?