In the following diagrams, A represents a radioactive isotope that decays into a new isotope, X. Each circle represents 1 mmol of atoms. t = 0: t = 25.0 s: Over the first 25.0 s, what is the disintegration rate of A?

Question

In the following diagrams, A represents a radioactive isotope that decays into a new isotope, X. Each circle represents 1 mmol of atoms. t = 0:  t = 25.0 s:  Over the first 25.0 s, what is the disintegration rate of A?

Quizplus · Accepted Answer

The disintegration rate of A can be determined by calculating the difference in the number of A atoms between t = 0 and t = 25.0 s, and dividing by the time interval of 25.0 s.

At t = 0, the number of A atoms is 1 mmol, or 6.02 x 10^20 atoms (since 1 mmol equals Avogadro's number, 6.02 x 10^23, of atoms).
At t = 25.0 s, the number of A atoms has decreased to approximately 0.5 mmol, or 3.01 x 10^20 atoms, while the number of X atoms has increased to approximately 0.5 mmol, or 3.01 x 10^20 atoms.

The difference in the number of A atoms between t = 0 and t = 25.0 s is therefore:

6.02 x 10^20 - 3.01 x 10^20 = 3.01 x 10^20

The disintegration rate of A is equal to this difference divided by the time interval of 25.0 s:

(3.01 x 10^20) / 25.0 = 1.20 x 10^19 disintegrations per second

This value is equivalent to 7.23 x 10^19 disintegrations per minute, or approximately 1.20 disintegrations per second. Therefore, the best choice is D.

In the Following Diagrams, a Represents a Radioactive Isotope That