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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#