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.

2 Answers
Apr 24, 2018

12.5 g

Explanation:

The basic formula for half life equations is

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(1/2)^(24/6)

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

:)

Apr 24, 2018

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

ln[A]_"t" = -kt + ln[A]_0, and by extension,

t_(1/2) = ln(2)/k

Now, let's derive the rate constant,

=> k = ln(2)/t_(1/2) approx 0.116"h"^-1

Given t = 6"h",

=>ln(([A]_"t")/([A]_0)) = -kt

=> [A]_"t" approx 12.5"g"

of technetium-99 will remain of the shipment.