Explanation Write the expression for decay rate or activity of the iron with the total mass of m . R m = ( R m ) 0 e − λ t (I) Here, R is the decay rate or activity of the iron, R 0 is the initial decay rate or activity of the iron at t = 0 , λ is the decay constant, m is the mass of the radioactive material and t is the time taken. Write the expression from half-life time. T 1 / 2 = 0.693 λ (II) Here, T 1 / 2 is the half-life time and λ is the decay constant. Rewrite the above expression for decay constant. λ = 0.693 T 1 / 2 (III) In this case, the radioactive iron 59 F e with a half-life of 45.1 d is included in the total mass is 0.200 kg . After a 1000 h test period, some of the lubricant oil is removed from the engine and found to contain enough 59 F e to produce 800 Bq/L of oil. The total volume of oil in the engine is 6.50 L . One Becquerel is equivalent to 1 disintegrations per second. Write the expression for the activity of the oil. R O i l = ( P ) ( V ) (IV) Here, R O i l is the activity of the oil, P is the decay production activity in decay/min/liter and V is the volume of the oil in the engine in liter . Write the expression for the mass of the oil, m O i l = R O i l ( R / m ) (V) Here, m O i l is the mass of the oil. Conclusion: Substitute 45.1 d for T 1 / 2 in the (III) to find λ value

Physics for Scientists and Engineers with Modern Physics, Technology Update

9th Edition

ISBN: 9781305401969

Author: SERWAY, Raymond A.; Jewett, John W.

Publisher: Cengage Learning

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Radioactive decay

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Artificial Radioactivity

The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.

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Chapter 45, Problem 71AP

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Physics for Scientists and Engineers with Modern Physics, Technology Update

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