Radioactive strontium-90, 90Sr, has a half-life of 28 years. Answer each of the

Question

Radioactive strontium-90, 90Sr, has a half-life of 28 years. Answer each of the following by entering a three (3) significant figure real number.

(a) What fraction of a sample of 90Sr will remain after three half-lives? the tolerance is +/-1 in the 3rd significant digit

(b) What fraction of a sample of 90Sr will remain after 185 years? the tolerance is +/-1 in the 3rd significant digit

(c) If the amount of 90Sr remaining in a sample is only one-thirtysecond of the amount originally present, how many years has the sample been undergoing radioactive decay? years

Explanation / Answer

at time t= 0 let the number of moles of Strontium N

After first half life, the concentration drops to 50% of its intitla value =N/2=0.5N

amount remained after 1st half life =0.5N

After second half life, amount remained =0.5N/2 =0.25N

After third half life, sample remained =0.25N/2 =0.125N

b) The decay obeys frist order equation for which half life t1/2 = 0.693/ K, K is the rate constant

K= 0.693/ t1/2 =0.693/28 =0.02475 yr-1

From N= No e-Kt

N= concentration at time 185 years

N= N0* e-0.02475*185 =No*e-4.57875 = 0.0102NO

1.02% of the sample remains

c) Origianally present N0

Amount present ,N =N0/130

N= N0 e-Kt

N/N0 =1/130 = e-Kt

ln(1/130)= -Kt

-ln(130)= Kt

t= ln(130)/K = ln(130)/ 0.02475 = 196. 6 yers

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