Technetium 99 is used for brain scans. If a laboratory receives a shipment of 200 g of this isotope, how much will remain after 24 hours? The half life of Technetium 99 is 6 hours.

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Answer 1 · 2018-04-24T00:46:15

12.5 g

The basic formula for half life equations is

$A = P {(\frac{1}{2})}^{\frac{t}{h}}$ $A=P(1/2)^(t/h)$

A= amount remaining
P= original amount
t= elapsed time
h=half life time

so just plug in your amounts
P=200
t=24
h=6

$A = 200 {(\frac{1}{2})}^{\frac{24}{6}}$ $A=200(1/2)^(24/6)$

when you put it into a calculator, you get 12.5 grams

:)

Answer 2 · 2018-04-24T00:57:00

Consider that radioactive decay follows first order kinetics. Thus, recall,

${ln [A]}_{t} = - k t + {ln [A]}_{0}$ $ln[A]_"t" = -kt + ln[A]_0$ , and by extension,

$t_{\frac{1}{2}} = \frac{ln (2)}{k}$ $t_(1/2) = ln(2)/k$

Now, let's derive the rate constant,

$\Rightarrow k = \frac{ln (2)}{t_{\frac{1}{2}}} \approx 0.116 h^{- 1}$ $=> k = ln(2)/t_(1/2) approx 0.116"h"^-1$

Given $t = 6 h$ $t = 6"h"$ ,

$\Rightarrow ln (\frac{{[A]}_{t}}{{[A]}_{0}}) = - k t$ $=>ln(([A]_"t")/([A]_0)) = -kt$

$\Rightarrow {[A]}_{t} \approx 12.5 g$ $=> [A]_"t" approx 12.5"g"$

of technetium-99 will remain of the shipment.