Question

If 190 mg of fluorine-18 is shipped at 10:00 A.M., how many milligrams of the radioisotope are still active when the sample arrives at the radiology laboratory at 5:20 P.M.? Express the mass to three significant figures and include the appropriate units.

A. 63.9 mg
B. 91.0 mg
C. 94.1 mg
D. 63.0 mg

Answer 1

The mass to three significant figures and include the appropriate units is 94.1 mg.The correct answer is C. 94.1 mg.

Step-by-step explanation:

The decay of a radioactive substance follows an exponential decay model given by the equation
`\(N_t = N_0 * e^(-kt)\),` where
`\(N_t\)` is the remaining quantity at time t ,
`\(N_0\)` is the initial quantity, k is the decay constant, and e is the base of the natural logarithm.

The decay constant K for fluorine-18 is approximately 0.0295 minutes⁻¹. Given that the time elapsed t from 10:00 A.M. to 5:20 P.M. is 7 hours and 20 minutes, or 440 minutes, we can substitute these values into the decay equation:

`\[N_t = 190 * e^(-0.0295 * 440)\]`

Calculating this expression yields the remaining quantity of fluorine-18 at 5:20 P.M. as approximately 94.1 mg, rounded to three significant figures. Therefore, the correct answer is option C.

In summary, the decay of fluorine-18 can be modeled using the exponential decay equation, and by substituting the given values, we determine that approximately 94.1 mg of the radioisotope remains active when the sample arrives at the radiology laboratory at 5:20 P.M. This calculation ensures accurate representation, considering both the decay constant and the elapsed time.

The correct answer is C. 94.1 mg.