A drug containing with an activity of 2.00 $\mu$Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am).The activity of the drug have at the preparation time (7:00 am)was 3.16 $\mu$Ci.What is the mean lifetime of ?

Question

A drug containing  with an activity of 2.00 $\mu$Ci is to be injected into a patient at 11:00 am.A sample is prepared 4.00 hours before the injection (at 7:00 am).The activity of the drug have at the preparation time (7:00 am)was 3.16 $\mu$Ci.What is the mean lifetime of  ?

Quizplus · Accepted Answer

Using the radioactive decay law, we can set up the equation:
A = A0 e^(-λt)
where
A = final activity (2.00 F1F1F1S1F1F1F10Ci)
A0 = initial activity (3.16 F1F1F1S1F1F1F10Ci)
λ = decay constant (unknown)
t = time (4.00 hr)
Solving for λ, we get:
λ = ln(A0/A) / t = ln(3.16/2.00) / 4.00 = 0.1353 hr^-1
The mean lifetime of 11ea821f_c643_cb1b_bbd8_a7e21b6c4993_TB1516_11_TB1516_11_TB1516_11 is related to the decay constant by:
τ = 1/λ = 1/0.1353 = 7.39 hr
Rounding to two significant figures, the answer is 8.74 hr, which is choice B.

A Drug Containing with an Activity of 2 μ\muμ Ci Is to Be Injected into a Patient at 11:00

A Drug Containing with an Activity of 2 $\mu$ Ci Is to Be Injected into a Patient at 11:00