SOLUTION: Phosphorous-24 is a radioactive isotope with a half life of 14.3 days. If you start with 33 grams of that substance, how long will it be before you have only 25 grams remaining? Da
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-> SOLUTION: Phosphorous-24 is a radioactive isotope with a half life of 14.3 days. If you start with 33 grams of that substance, how long will it be before you have only 25 grams remaining? Da
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Question 767958: Phosphorous-24 is a radioactive isotope with a half life of 14.3 days. If you start with 33 grams of that substance, how long will it be before you have only 25 grams remaining? Days (2 decimals): Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website! Formula: A(t) = A(o) e ^kt
A(t) active amount left
A(o) active amount started with
k = exponential constant of proportionality
t = time interval involved.
To work out 'k'
Calculate 1/2 life
A(t) = A(o) e ^kt
A(t)/A(o) = 1/2
1/2 =e^kt
1/2 = e^k(14.3) insert half life
Take natural logs of both sides.
ln (1/2) = 14.3 k ln e (ln e = 1)
ln (1/2)/14.3 = k
k = -0.04847
..............
Set up formula:
A(t) = A(o) e ^-0.04847t
25 = 33 e^-0.04847t
25/33 = e^-0.0487t
Natural logs of both sides
ln(25/33) = -0.0487t ln e
ln(25/33)/-0.0487 = t
t = 5.70 days.
Hope this helps.
:-)
