(a) 5 x 365 = 1865 days

1865/138 = 13.22 half lives

amount remaining = A = initial amount x fraction decayed

200 x (1/2^13.22 ) = 0.021g

(b) fraction decayed = 90/200 = 0.45

half lives =0.45/0.5 = 0.9 half lives or 0.9 x 138 = 124.2 days

call the half life : f

in time t there will have been t/f times the sample has halved by 2, and leaves:

N(t) = No / 2^(t/f)

No = amount at time t =0

a)

5 years = 365×5 days = 1825 days

N(1825) = 200/ 2^(1825/138) = 0.0209 g = 20.96 mg

b)

ln(N) = ln(No) – t/f ln(2)

t = f (ln(No) – ln(N)) /ln(2)

= 138(ln(200)-ln(110) ) /ln(2)

= 16425 days = 45 years ????????

this doesn’t make much sense (sorry!)

a) .006104 grams

b)124.2 days

answer b= 289.8 days