carbon-14 has a half - life of 5,730 years. if a sample originally contained 25.0 g of carbon - 14, what…

Explanation:

Step1: Calculate number of half - lives

The number of half - lives $n=\frac{17190}{5730}=3$.

Step2: Use half - life formula

The formula for radioactive decay is $m = m_0\times(\frac{1}{2})^n$, where $m_0 = 25.0$ g is the initial mass and $n$ is the number of half - lives. Substitute $m_0 = 25.0$ g and $n = 3$ into the formula: $m=25.0\times(\frac{1}{2})^3$.

Step3: Calculate the remaining mass

$m = 25.0\times\frac{1}{8}=3.125\approx3.13$ g.

Answer:

3.13 g