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The activity of a radioactive sample is the number of
Chapter 14, Problem 126AP(choose chapter or problem)
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 \(3.70 \times 10^{10}\) disintegrations per second. This decay rate is equivalent to that of 1 g of radium-226. Calculate the rate constant and half-life for the radium decay. Starting with 1.0 g of the radium sample, what is the activity after 500 yr? The molar mass of Ra-226 is 226.03 g/mol.
Questions & Answers
QUESTION:
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 \(3.70 \times 10^{10}\) disintegrations per second. This decay rate is equivalent to that of 1 g of radium-226. Calculate the rate constant and half-life for the radium decay. Starting with 1.0 g of the radium sample, what is the activity after 500 yr? The molar mass of Ra-226 is 226.03 g/mol.
ANSWER:Step 1 of 4
We are asked to find the rate constant and the half-life of Radium decay for 1 gram of radium. We are also asked to find the activity of a Ra-226 Radium sample after 500 years.
Given:
Atomic mass of Ra-226:226.03 g/mol.
Mass of radium sample:1g
Avogadro’s number: \(6.022 \times 10^{23}\)
\(\mathbf{1 C i}=3.7 \times 10^{10} \text { disintegrations } / s\)