An unknown radioactive substance has a half-life of 3.20 hours. If 47.8 g of the

Question

An unknown radioactive substance has a half-life of 3.20 hours. If 47.8 g of the substance is currently present, what mass A_0 was present 8.00 hours ago? Express your answer with the appropriate units. 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 31.0 % of an Am-241 sample to decay? Express your answer with the appropriate units. 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? Express your answer with the appropriate units.

Explanation / Answer

All radioactive decay follow first order kinetics. The rate expression for first order reactions is

k = [2.303/t ] log (a/a-x) where k is the decay constant, t is the time elapsed, a -the initial concentration, a-x the remaining concentration

Part B

Given t1/2 = 3.20hr and hence k = 0.693/3.2 t= 8.00hr and a-x = 47.8g

substituting the given values

o.693/3.2 = (2.303/8.0 ) log a/47.8

we get a (Ao) = 270.16g

Part C

T1/2 = 432yr and 31% is decayed.

time = (2.303x432/0.693) log (100/69) = 231.23 yr

Part D

t1/2 = 5730yr and 20% remaining

time = (2.303x5730/0.693) log (100/20 )= 13310 yr

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.