First Order Half Life Video Lessons

Concept:

# Problem: A sample of F-18 has an initial decay rate of 1.6×105 /s .How long will it take for the decay rate to fall to 2.6×103 /s ? (F-18 has a half-life of 1.83 hours.)

###### FREE Expert Solution

We’re being asked to determine the time will it take for the decay rate of F-18 to fall to 2.6x103/s.

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

$\overline{){\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{0}}}}$

where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration.

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###### Problem Details

A sample of F-18 has an initial decay rate of 1.6×105 /s .

How long will it take for the decay rate to fall to 2.6×103 /s ? (F-18 has a half-life of 1.83 hours.)