Final answer:
After 5 half-lives, only 3.125% of a radioactive substance typically remains. For a 165.0g sample, this means 5.15625g will be left.
Step-by-step explanation:
To find out how much of a 165.0g sample will remain after 5 half-lives, we can use the concept of radioactive decay. With each half-life, the amount of the substance remaining is halved. So after one half-life, half of the original substance would remain, after two half-lives, one quarter would remain, and this pattern continues.
Following this pattern:
- After 1 half-life, 50% remains
- After 2 half-lives, 25% remains (half of 50%)
- After 3 half-lives, 12.5% remains (half of 25%)
- After 4 half-lives, 6.25% remains (half of 12.5%)
- After 5 half-lives, 3.125% remains (half of 6.25%)
To calculate the exact amount remaining after 5 half-lives, we multiply the initial amount by 3.125%:
165.0g × 0.03125 = 5.15625g
Therefore, 5.15625g of the sample will remain after 5 half-lives.