Question

Nuclear decay occurs according to first-order kinetics. How long will it take for a sample of radon-218 to decay from 99 grams to 0. 50 grams? the half-life of radon-218 is 35 milliseconds.

Answer 1

It will take 267 milliseconds for a sample of radon-218 to decay from 99 grams to 0. 50 grams.

We know that half life of a first order reaction is given by: $t_{1/2} = 0.693/k$

where k = rate of reaction

Given half life = 35 milliseconds

So from this we get k = 0.0198

Now we know that rate of first order reaction is given by: $kt= 2.303 * log(R'/R)$

where t= time

R'= initial amount = 99 g

R= final amount= 0.50 g

k= rate of reaction = 0.0198

Putting values of these in above equation we get t=267 milliseconds.

i.e. It will take 267 milliseconds for a sample of radon-218 to decay from 99 grams to 0. 50 grams.

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