You have 180g of a radioactive substance. It has a half-life of 265 years. After 1,325 years, what mass
remains?
The formula to calculate the remaining mass of a radioactive substance after a certain period of time is given by:
Mass remaining = Initial mass × (1/2)^(time elapsed / half-life)
In this case, we are given an initial mass of 180g, a half-life of 265 years, and a time elapsed of 1,325 years. Now, let's substitute these values into the formula to solve for the remaining mass:
Mass remaining = 180g × (1/2)^(1325 years / 265 years)
We can simplify this as:
Mass remaining = 180g × (1/2)^5
Now, let's calculate the value of (1/2)^5:
(1/2)^5 = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32
Substituting this value back into the equation:
Mass remaining = 180g × 1/32
Finally, let's calculate the remaining mass:
Mass remaining = 5.625g
Therefore, after 1,325 years, approximately 5.625g of the radioactive substance remains.