Question

How long will it take a 200.00 mg sample of potassium-38 to be reduced to 25.00 mg if its half-life is 7.7 minutes?

A) 15.4 minutes
B) 30.8 minutes
C) 46.2 minutes
D) 61.6 minutes

Answer 1

It will take 23.1 minutes for the sample of potassium-38 to be reduced to 25.00 mg.

Step-by-step explanation:

To determine how long it will take for a sample of potassium-38 to be reduced to 25.00 mg, we need to calculate the number of half-lives that have occurred. Each half-life is 7.7 minutes, so we can divide the initial mass by 2 for each half-life until we reach the desired mass:

200.00 mg / 2 = 100.00 mg (1 half-life)

100.00 mg / 2 = 50.00 mg (2 half-lives)

50.00 mg / 2 = 25.00 mg (3 half-lives)

Since it took 3 half-lives to reach 25.00 mg, the answer is 3 x 7.7 minutes = 23.1 minutes.