Question
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.
Express your answer to two significant figures and include the appropriate units.
Answers
GPT 3.5
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.
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.