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(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

:)

Answer 2 · 2018-04-24T00:57:00

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.