# 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?

### 3 Answers

- 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)

where

.. 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.