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Answer 1 · 2016-03-02T19:36:15

$45"min"$

The equation for radioactive decay is:

$N_t=N_0e^(-lambda"t")$

$N_0$ is the initial number of undecayed atoms.

$N_t$ is the number of undecayed atoms after time $t$ .

$lambda$ is the decay constant.

We can say that $N_0$ represents 100% of undecayed atoms.

If 34% decay then there must be 100 - 34 = 66% atoms remaining.

$:.66=100e^(-lambda"t")$

$:.ln66=ln100-lambda"t"$

$:.lambda"t"=ln100-ln66$

$:.lambda=(4.605-4.19)/27=0.0514"min"^(-1)$

$t_(1/2)=0.693/lambda$

$:.t_(1/2)=0.693/0.0514=45"min"$