If a sample of iodine-131 contains 4.5 ×10^16 nuclei, what is the activity of the sample? Expres

step 1 As we all know that lambda is equal to 0 .693 by t half. So simplifying it further, first time j

If a sample of iodine-131 contains 4.5 ×10^16 nuclei, what...

If a sample of iodine-131 contains $4.5 \times 10^{16}$ nuclei, what is the activity of the sample? Express your answer in curies.
A. $0.27 \mathrm{Ci}$
B. $1.2 \mathrm{Ci}$
C. $1 .7 \mathrm{Ci}$
D. $4.5 \mathrm{Ci}$

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Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting ionizing particles or radiation. The decay follows an exponential law, where the number of nuclei decreases over time, and is characterized by a constant probability of decay per unit time.

Activity

Activity is a measure of the rate at which radioactive nuclei decay in a sample, expressed in disintegrations per second. It reflects how quickly the nuclei are decaying at any given moment and is directly proportional to both the decay constant and the number of radioactive atoms present.

Decay Constant

The decay constant is a property of a radioactive isotope that establishes the probability per unit time that a nucleus will decay. It is inversely related to the half-life of the isotope, and when multiplied by the number of nuclei, it yields the activity of the sample.

Unit Conversion of Radioactivity

In radiochemistry, activity can be expressed in various units, with the curie being a common one. The curie is defined based on a specific number of disintegrations per second, and converting between units like disintegrations per second (becquerels) and curies is crucial for comparing the radioactivity of different samples.

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