Question 191308
Radium-226 is a radioactive element with a half-life of 1600 years. 
How much of a 1000 g sample of the element will be present after 6400 years?
:
The half-life decay formula: A = Ao(2^(-t/h))
where:
Ao = initial amt
A = resulting amt after t years
h = half-life of substance
t = time in years
:
A = 1000(2^(-6400/1600))
A = 1000(2^-4)
A = 1000 * .0625
A = 62.5 grams after 6400 yrs
:
:
How long will it take for the 1000 gram sample to decay to 1 gram?
1 = 1000(2^(-t/1600))
Divide both sides by 1000 and we can write this: 
2^(-t/1600) = {{{1/1000}}}
2^(-t/1600) = .001
log(2^(-t/1600)) = log(.001)
{{{-t/1600}}}*log(2) = log(.001)
 {{{-t/1600}}}*.30103 = -3
Multiply both sides by 1600, results
-.30103t = -4800
t = {{{(-4800)/(-.30103)}}}
t = 15,945.25 yrs for 1000 g to decay to 1 g
;
:
Check by using this in the following equation with a calc
A = 1000(2^(-15945.25/1600))
A = 1.000; confirms our solution