Item 6 If a substance is radioactive, this means that the nucleus is unstable an

Question

Item 6 If a substance is radioactive, this means that the nucleus is unstable and will therefore decay by any number of processes (alpha decay, beta decay, etc.). The decay of radioactive elements follows first-order kinetics. Therefore, the rate of decay can be described by the same integrated rate equations and half-life equations that are used to describe the rate of first-order chemical reactions. By manipulation of these equations, we can arrive at the following formula: fraction remaining (0.5) where Ao is the initial amount or activity, Ais the amount or activity at time t, and n is the number of half-lives. The equation relating the number of half- lives to time t is where t 1/2 is the length of one half-life. Part 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 31.7 minutes, what is the half-life of this substance? Express your answer numerically in minutes. minutes 1/2 Submit Hints My Answers Give Up Review Part Part B An unknown radioactive substance has a halflife of 3.20 hours. If 15.9 g of the substance is currently present, what mass Ao was present 8.00 hours ago? Express your answer numerically in grams. Submit Hints My Answers Give Up Review Part

Explanation / Answer

according to first law

part A

K = 0.693 /t1/2

K = (1/t)ln(a0/a)

a0 = initial amount

a = after t time amount

k = (1/31.7)ln((400/100) = 0.0437 min-1

t1/2 = 0.693/0.0437 = 15.86 min

part B

k = 0.693 /t1/2 = 0.693/3.2 = 0.216 hr-1

K = (1/t)ln(a0/a)

t = 8 hr

a = 15.9 , a0 = ?

0.216 = (1/8)ln(x/15.9)

a0 = 89.5 g

part C

k = 0.693/432 = 0.0016 y-1

k = (1/t)ln(a0/a)

0.0016 = (1/t)ln(100/34)

t = 674.26 years

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