Question

Technetium-99m, a radioisotope used to image the skeleton and the heart muscle, has a half-life of about 6 hours.

Find the decay constant. Use the decay function
N(t)=N0e−kt
to determine the amount of a 250 mg dose that remains after 24 hours.

Answer 1

I can not stay on for too long, but whoever comes across this question of mine, please help me out, I really want to know how to do this. Thanks

Answer 2

\[N(t) = N_0e^{-kt}=N_0(\tfrac12)^{\frac t{t_{1/2}}}\]
\[e^{-k} = (\tfrac12)^{\frac1{t_{1/2}}}\\
-k = \ln(\tfrac12)^{\frac1{t_{1/2}}}\\
-k = \frac1{t_{1/2}}\ln(\tfrac12)\\
k = \frac{\ln 2}{t_{1/2}}\]

Answer 3

Alright thanks, I appreciate it. :)

Answer 4

If the question hadn't specifically asked you to use the exponential form of the decay function, the second question would have simpler
\[N(24\,\text{hr})=250\,\text{mg}\cdot(\tfrac12)^{24\,\text{hr}/6\,\text{hr}}\\
\qquad\quad=250\,\text{mg}\cdot(\tfrac12)^4\\
\qquad\quad=\frac{250\,\text{mg}}{2^4}\\
\qquad\quad=\frac{250\,\text{mg}}{16}\]

Answer 5

You should get the same result anyway.