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Answer 1 · 2017-05-23T06:12:48

The half life is $= 126.6 s$ $=126.6s$

The equation of the radioactive decay is

$M (t) = M_{0} \cdot e^{- λ t}$ $M(t)=M_0*e^(-lambdat)$

The initial mass is $M_{0} = 300 g$ $M_0=300g$

The final mass is $M_{t} = 112 g$ $M_t=112g$

The time is $t = 180 s$ $t=180s$

The radioactive constant is $= λ$ $=lambda$

Therefore,

$112 = 300 \cdot e^{- 180 λ}$ $112=300*e^(-180lambda)$

$e^{- 180 λ} = \frac{112}{300} = 0.373$ $e^(-180lambda)=112/300=0.373$

$e^{180 λ} = \frac{1}{0.373} = 2.679$ $e^(180lambda)=1/0.373=2.679$

$180 λ = ln (2.6790) = 0.985$ $180lambda=ln(2.6790)=0.985$

$λ = \frac{0.985}{180} = 0.0055$ $lambda=0.985/180=0.0055$

But

$λ = \frac{0.693}{t_{\frac{1}{2}}}$ $lambda=0.693/t_(1/2)$

So,

The half life is

$t_{\frac{1}{2}} = \frac{0.693}{λ} = 126.6 s$ $t_(1/2)=0.693/lambda=126.6s$