Question

It has a half-life of approximately 6 hours. If a patient is given 1000 mg for a procedure, in how many hours will 62.5 mg of technetium-99 remain in the bloodstream?

A) 3 hours.
B) 12 hours.
C) 24 hours.
D) 18 hours.

Answer 1

To calculate the time for a 1000 mg dose of technetium-99 to decay to 62.5 mg, we determine it takes 4 half-lives, and since each half-life is 6 hours, the total time is 24 hours.

Step-by-step explanation:

The question asks us to calculate the time it will take for a 1000 mg dose of technetium-99 to decay to 62.5 mg in the bloodstream, given that the substance has a half-life of approximately 6 hours. To find the number of half-lives needed to reach 62.5 mg from 1000 mg, we can divide 1000 mg by 2 repeatedly until we reach or go below 62.5 mg.

• 1000 mg ÷ 2 = 500 mg (1 half-life)
• 500 mg ÷ 2 = 250 mg (2 half-lives)
• 250 mg ÷ 2 = 125 mg (3 half-lives)
• 125 mg ÷ 2 = 62.5 mg (4 half-lives)

Since each half-life is 6 hours, we can calculate the total time by multiplying the number of half-lives by the duration of one half-life: 4 half-lives × 6 hours/half-life = 24 hours. Therefore, it will take 24 hours for the dose to reduce to 62.5 mg in the bloodstream.