Curium has a half life of 1.5 hours, how much of a 1000g sample remains after: 1.5 hrs? 3hrs? 4.5 hrs? 6hrs?

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Answer 1 · 2018-06-19T13:02:08

Let's assume the radioactive decay of curium follows first-order kinetics.

Given,

#t_(1/2) = 1.5"hr"#

#[A]_0 = 1000"g"#

Recall,

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

#ln(([A]_"t")/([A]_0)) = -kt" "(2)#

Let's derive the rate constant,

#=> k = ln(2)/t_(1/2) approx 0.462"hr"^-1#,

and rearrange (2),

#[A]_"t" = [A]_0e^(-kt)#

Hence,

puu.sh

is how your data would work out.

Note: I used a relatively advanced method to solve this, lots of beginning chemistry students use simple arithmetic,

#(1/2)^n#, where #n = t/t_(1/2)#