The half life of a certain radioactive element is 800 years. How old is an object if only 12.5% of the radioactive atoms in it remains?

Given, half life of a certain radioactive element = 800 years.

Amount of substance remaining at time t = 12.5%

Lets consider the initial amount of the radioactive substance = 100%

Using the half life equation:

A = A₀ (1/2) ^t/t₁/₂

where A₀ is the amount of radioactive substance at time zero and A is the amount of radioactive substance at time t, and t₁/₂ is the half-life of the radioactive substance.

Plugging the given data into the half life equation we have,

12.5 = 100. (1/2) ^t/800

12.5/100 = (1/2) ^t/800

0.125 = (0.5) ^t/800

(0.5) ^3 = (0.5) ^t/800

3 = t/800

t = 2400 years

Thus the object is 2400 years old.