Explanation If we consider after starting the radioactive disintegration of a certain nucleus after the time gap ‘t’ the number of atom disintegrate is ‘N’. Then for small gap of time ‘dt’ the disintegration of the atom will be ‘dN’. Then as per the law of radioactive disintegration the rate of decay ( − d N d t ) of the atom will be equivalent to the number of atom present at the moment. so, − d N d t ∞ N or, − d N d t = λ N (Where λ is a constant called disintegration constant or decay constant). The value of the decay constant is fixed for a radioactive material. The half life time of a radioactive material is the time required to disintegrate half of the material. It is expressed by: t 1 / 2 = 0.693 λ Given Info: The half-life of 238 U is 4.5 × 10 9 yr. The sample of rock of mass 1.6g produces 29 dis/s. Formula used: − d N d t = λ N , t 1 / 2 = 0.693 λ , 1curie (C) = 3.7 × 10 10 dis/s or dps Calculation: We know 1curie(C) = 3.7 × 10 10 dis/s or dps,so, 29 dps = 29 3.7 × 10 = 7.837 × 10 − 10 C So, the rate of dissociation − d N d t = 7.837 × 10 − 10 …………Equation 1 The dissociation constant λ = 0.693 t 1 2 so, from the given data the dissociation constant is λ = 0...

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Writing and Balancing Nuclear Equations

A nuclear equation is a symbolic representation of a nuclear reaction using certain symbols. It is studied in nuclear chemistry and nuclear physics.

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Chapter 20, Problem 91E

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To determine: The percent of mass of ²³⁸U in the rock.

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Chapter 20, Problem 90E

Chapter 20, Problem 92E

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