Question #21f9a

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Answer 1 · 2016-10-28T02:20:36

1.2 grams

Let n = the number of half lives

Let Q(n) = the quantity after n half lives.

Let Q(0) = the original quantity

The exponential decay is
#Q(n) = Q(0)e^(alpha(n))#

when #n = 1#:

#(Q(1))/(Q(0)) = 1/2#

This helps us to find the value of #alpha#

#1/2 = e^(alpha(1))#

#ln(1/2) = alpha#

#alpha = -ln(2)#

#Q(n) = Q(0)e^(-ln(2)n)#

Your conditions are Q(0) = 75.0 g and n = 6

#1.2 g = (75.0 g)e^(-ln(2)6)#