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
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
CONNECT F/CHEMISTRY+ALEKS 1 SEMESTER
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- Iodine-131 is used to treat tumors in the thyroid. Its decomposition is first-order with a half-life of 8.1 days. If a patient is given a sample containing 5.00 mg of I-131, how long will it take for 32% of the isotope to remain in her system?arrow_forwardSucrose, a sugar, decomposes in acid solution to give glucose and fructose. The reaction is first-order in sucrose, and the rate constant at 25 C is k = 0.21 h1. If the initial concentration of sucrose is 0.010 mol/L, what is its concentration after 5.0 h?arrow_forwardMany biochemical reactions are catalyzed by acids. A typical mechanism consistent with the experimental results (in which HA is the acid and X is the reactant) is Step 1: Step 2: Step 3: Derive the rate law from this mechanism. Determine the order of reaction with respect to HA. Determine how doubling the concentration of HA would affect the rate of the reaction.arrow_forward
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