To find the fraction of the original amount of radium-226 that will still be radium after 8,000 years, we can use the formula for radioactive decay:
Fraction remaining = (1/2)^(t/half-life)
Where:
t is the time in years.
half-life is the half-life of the substance.
In this case, the half-life of radium-226 is 1,600 years, and you want to find the fraction remaining after 8,000 years. Plugging these values into the formula:
Fraction remaining = (1/2)^(8000/1600)
Fraction remaining = (1/2)^5
Fraction remaining = 1/32
So, after 8,000 years, 1/32 of the original amount of radium-226 will still be radium. Therefore, the answer is C.