Phosphorus-32 is radioactive and has a half life of 14.3 days. How long would it take a sample to decay from 2.20 mg to 600 #mu#g?

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Answer 1 · 2016-11-01T20:05:27

26.8 days.

The equation for 1st order decay is:

#sf(N_t=N_(0)e^(-lambdat))#

We can get the value of the decay constant #sf(lambda)# from the 1/2 life:

#sf(lambda=0.693/t_(1/2)=0.693/14.3=0.0484color(white)(x)d^(-1))#

Taking natural logs of both sides:

#sf(lnN_t=lnN_0-lambdat)#

Putting in the numbers and converting to milligrams:

#sf(ln0.6=ln2.2-0.0484t)#

#:.##sf(-0.5108=0.7884-0.0484t)#

#:.##sf(t=1.30/0.0484=26.8color(white)(x)"days")#