Problema Solution
The half-life of a certain radioactive element is 1,250 years. What percent of the atoms remain after 7,500 years?
Answer provided by our tutors
The formula for determining the amount of substance left is:
A=Ce^(kt), where C is the initial amount, k is the decay constant, and t is time.
Given the half-life of 1,250 years we have:
C/2=Ce^(1250k)
½=e^(1250k)
ln(1/2)=ln(e^(1250k)
-0.693=1250k
k=-0.693/1250
k=-0.0005544
Amount after t = 7,500 years:
A=C*e^(-0.0005544*7500)
A=Ce^(-4.158)
A=0.01564C
After 7,500 years there will be 1.564% left.