Question

bonus: after 4 half - lives, a sample of polonium - 218 has a mass of 12 grams. what was the original mass of the sample? the half - life of polonium - 218 is 3.1 minutes. support your answer.

Explanation:

Step1: Recall half - life formula

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

Step2: Identify given values

We know that $m = 12$ grams, $n = 4$.

Step3: Solve for $m_0$

Substitute the values into the formula: $12=m_0(\frac{1}{2})^4$. Rearranging for $m_0$, we get $m_0=\frac{12}{(\frac{1}{2})^4}$. Since $(\frac{1}{2})^4=\frac{1}{16}$, then $m_0 = 12\times16$.

Step4: Calculate $m_0$

$m_0=192$ grams.

Answer:

192 grams