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Answer 1 · 2017-05-23T06:12:48

The half life is $=126.6s$

The equation of the radioactive decay is

$M(t)=M_0*e^(-lambdat)$

The initial mass is $M_0=300g$

The final mass is $M_t=112g$

The time is $t=180s$

The radioactive constant is $=lambda$

Therefore,

$112=300*e^(-180lambda)$

$e^(-180lambda)=112/300=0.373$

$e^(180lambda)=1/0.373=2.679$

$180lambda=ln(2.6790)=0.985$

$lambda=0.985/180=0.0055$

But

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

So,

The half life is

$t_(1/2)=0.693/lambda=126.6s$