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.