Question

the half - life of element x is 500 years. if there are initially 8 g of x, how much will remain after 1500 years?

Explanation:

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{1500}{500}=3$.

Step2: Use half - life formula

The formula for radioactive decay is $m = m_0\times(\frac{1}{2})^n$, where $m_0$ is the initial mass and $n$ is the number of half - lives. Here, $m_0 = 8$ g and $n = 3$. So $m=8\times(\frac{1}{2})^3$.

Step3: Calculate the remaining mass

$m = 8\times\frac{1}{8}=1$ g.

Answer:

1 g