The disintegration of radioactive phosphorus to silicon follows the first order kinetics with rate constant k\(_1\) = 3.85 x 10\(^{-3}\). Determine the half life of phosphorus.
Firstly, State the formula for the half-life of a first-order reaction.
Radioactive decay follows first-order kinetics.
The half-life (t\(_{1/2}\)) for a first-order reaction is related to the rate constant (k) by the formula:
t\(_{1/2}\) = \(\frac{ln 2}{k}\)
t\(_{1/2}\) ≈ \(\frac{0.693}{k}\)
Secondly, calculate the half-life using the assumed rate constant given in the question as k = 3.85 x 10\(^{-3}\)s\(^{-1}\)
t\(_{1/2}\) = \(\frac{0.693}{3.85 x 10\(^{-3}}\)
t\(_{1/2}\) = 180 s
There is an explanation video available below.
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