Question

A 115 mCi radioactive tracer is made in a nuclear reactor. When it is delivered to a hospital 16 hours later its activity is 95 mCi. The lowest usable level of activity is 10 mCi.

a. What is the tracer’s half-life?

b. For how long after delivery is the sample usable?

Short answer

Activity of a radioactive substance after a time t

R=R_o$e^{-\lambda u}$

Here, t is the time, R is final activity and R_o is initial activity, and is the disintegration constant.

Step-by-step solution

Substitute 115 mCi for Ro 95 mCi for R95 mCi115 mCie-λue-λu=0.826λ=0.19tλ= 0.011875 h-1

here it is.

The half-time is

Therefore,

$$\begin{gathered} T=\frac{0.693}{\lambda } \\ Substitute0.011875h^{-1}for\lambda \\ T=58.35h \\ Therefore,thehlftimeis58.35h \end{gathered}$$