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The activity of a radioactive sample is the number of nuclear disintegrations per second, which is equal to the first-order rate constant times the number of radioactive nuclei present. The fundamental unit of radioactivity is the curie (Ci). where 1 Ci corresponds to exactly
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Interpretation:
The rate constant and half-life for radium decay is to be calculated. Also, the activity of the radium sample after
Concept introduction:
Rate constant for a reaction is the proportionality constant, which relates the rate of reaction and the concentration of reactants in the reaction.
Half-life is the time required by a substance to reduce by half of its original quantity. Half-life for a substance can be calculated as follows:
Here,
Answer to Problem 126AP
Solution: Rate constant and half-life for radium decay is
Explanation of Solution
Given information: A
To determine the rate constant for the radium decay, the number of radium nuclei in
Now, calculate rate constant from the activity and the number of nuclei as follows:
Activity
Here,
Rearrange the equation to determine therate constant.
Substitute values of activity and number of nuclei in the above expression as,
The half-life of radium is determined as follows:
Substitute the value of rate constant in the above equation,
The activity of radium after
Now, by using the first-order integrated rate law, the number of nuclei remaining after
Here, Nt is the number of nuclei at the given time,
Substitute values of
Now, the activity of radium sample after
The rate constant and half-life for the radium decay is
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Chapter 14 Solutions
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