- #1

utkarshakash

Gold Member

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## Homework Statement

The mean life of a certain radioactive element is 6 hrs. By what fraction will its initial activity decrease over a time period of 5 hrs.

## Homework Equations

[itex]t_{avg}[/itex]=[itex]\frac{1}{k}[/itex]

Initial Activity = kN[itex]_{0}[/itex]

Final Activity = kN[itex]_{t}[/itex]

## The Attempt at a Solution

From eqn 1 I obtain the value of k = 0.166 hr[itex]^{-1}[/itex]

Since I have to calculate the fraction of initial and final activity

Dividing eqn 2 by 3

[itex]\frac{Initial Activity}{Final Activity}[/itex]=[itex]\frac{N_{0}}{N_{t}}[/itex]

So this means now I have to calculate [itex]\frac{N_{0}}{N_{t}}[/itex] which will be my answer

So using first order kinetics equation

k=[itex]\frac{2.303}{5}[/itex]log[itex]\frac{N_{0}}{N_{t}}[/itex]

Plugging the known values I get [itex]\frac{N_{0}}{N_{t}}[/itex]=2.3006

which is unfortunately incorrect. But how?