A) You are using a Geiger counter to measure the activity of a radioactive subst

Question

A) You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 62.6minutes , what is the half-life of this substance?

B) An unknown radioactive substance has a half-life of 3.20hours . If 41.9g of the substance is currently present, what mass A0 was present 8.00 hours ago?

C) Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years. How long will it take in years for 45.0% of an Am-241 sample to decay?

D) A fossil was analyzed and determined to have a carbon-14 level that is 20% that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil?

Explanation / Answer

A)Here, [A0]=400

[A]=100

Time, t=62.6 min

ln([A]/[A0])=-kt

ln(1/4)=-k*62.6

k=0.0221 min-1

Half life=0.693/k=0.693/0.0221

=31.3 min

B)T1/2=3.20hrs

k=0.693/T1/2=0.693/3.20=0.217 hrs-1

[A]=41.9g

ln([A]/[A0])=-kt

ln(41.9/[A0])=-0.217*8

41.9/[A0]=0.177

[A0]=236.9g

C)t1/2=432 yrs

k=0.693/432=1.604*10-3 yrs-1

[A]=0.45[A0]

[A]/[A0]=0.45

ln([A]/[A0])=-kt

ln0.45=-1.604*10-3t

t=497.8yrs

D)t1/2=5730 yrs

k=0.693/5730=1.209*10-4 yrs-1

[A]=0.20[A0]

[A]/[A0]=0.20

ln([A]/[A0])=-kt

ln0.20=-1.209*10-4t

t=13,307yrs

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