A 130-mg sample of technetium-99 m is used for a diagnostic test. If technetium-99 m has a half-life of 6.0 h, how many milligrams of the technetium-99 m sample remains active 30 h after the test?

Express your answer to two significant figures and include the appropriate units.

1 answer

To solve this problem, we can use the half-life formula:

N = N0 * (1/2)^(t/T)

Where:
N is the amount of the sample remaining after time t
N0 is the initial amount of the sample
t is the elapsed time
T is the half-life of the sample

In this case, N0 is 130 mg, t is 30 h, and T is 6.0 h. Plugging these values into the formula, we can find N:

N = 130 mg * (1/2)^(30/6.0)

N = 130 mg * (1/2)^5

N = 130 mg * 1/32

N = 4.0625 mg

So, approximately 4.1 mg of the technetium-99 m sample remains active 30 h after the test.