Half-Life World Problem?
The first atomic explosion was detonated in a desert in New Mexico on July 16, 1945. What fraction of the strontium-90 (half life=28.8 years) originally produced by that explosion still remains as of July 16, 2004?
- Dr WLv 73 weeks ago
I tend to use this equation for all my half life type problems
.. A(t) = A(o) * (1/2)^(t / half life)
.. A(t) = amount remaining after "t" time has elapsed
.. A(o = initial amount
.. t = elapsed time
.. half life = .... you guessed it.. half life
your question asks for the "fraction remaining". that means you want A(t) / A(o)
rearranging that above equation
.. A(t) / A(o) = (1/2)^(t / half life)
.. fraction remaining = (1/2)^( (2004-1945 yrs) / 28.8 yrs) = 0.24
- pisgahchemistLv 73 weeks ago
Nuclear decay ....
Nuclear decay follows first order kinetics, and the integrated rate equation is ...
N =No e^(-kt) ............ where k = decay constant (also λ)
The decay constant is related to the half-life: k=ln2 / t½
N/No = e^(-ln2 x t / t½)
N/No = e^(-ln2 x 59yr / 28.8yr)
N/No = 0.242
- Roger the MoleLv 73 weeks ago
July 16, 2004 - (July 16, 1945) = 59 years
(1/2)^(59 y / 28.8 y) = 0.24
So about 1/4 remains.