Answer:
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of Cs-131 is 30 years. After 120 years, which is equivalent to four half-lives (120 years / 30 years/half-life = 4 half-lives), the original mass of Cs-131 would have been halved four times.
Let’s say the original mass of the Cs-131 sample is M. After one half-life, the remaining mass would be M/2. After two half-lives, the remaining mass would be (M/2)/2 = M/4. After three half-lives, the remaining mass would be (M/4)/2 = M/8. And after four half-lives, the remaining mass would be (M/8)/2 = M/16.
Since we know that after four half-lives (120 years), 6.0 g of Cs-131 remain, we can set up an equation to solve for the original mass M: M/16 = 6.0 g. Solving for M, we find that M = 16 * 6.0 g = 96 g.
Therefore, the original mass of the Cs-131 sample was 96 grams.
Step-by-step explanation: