The half-life of cobalt-60 is 5.2 years. Find the time it would take for a sample of 0.5 grams to decay to 0.1 gram?

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Answer 1 · 2017-02-16T06:04:16

$sf(12.8)$ years

The equation for 1st order decay is:

$sf(M_t=M_0e^(-lambdat))$

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

$:.$ $sf(lambda=0.693/5.2=0.126color(white)(x)a^(-1))$

Taking natural logs of both sides:

$sf(lnM_t=lnM_0-lambdat)$

$:.$ $sf(ln[M_t/M_0]=-lambdat)$

$sf(ln[0.1/0.5]=-0.126xxt)$

$:.$ $sf(-1.609=-0.126xxt)$

$sf(t=1.609/0.126=12.77color(white)(x)a)$