Atoms And Nuclei Question 387
Question: A container is filled with a radioactive substance for which the half- life is 2 days. A week later, when the container is opened, it contains 5 g of the substance. Approximately how many grams of the substance were initially placed in the container?
Options:
A) 40
B) 60
C) 80
D) 100
Show Answer
Answer:
Correct Answer: C
Solution:
- For this substance 7 days correspond to $ 3.5 $ half- lives. Over 3 half- lifes the sample reduces to $ \frac{1}{2^{3}}=\frac{1}{8} $ of its initial mass. After 4 half- lifes, the sample has only $ \frac{1}{2^{4}}=\frac{1}{16} $ of its initial mass. Hence, after $ 3.5 $ half- lives the sample must contain somewhere between $ 1/8 $ and $ 1/16 $ of its initial mass. Hence 5 g is somewhere between 1/8 and $ 1/16 $ of the initial mass. So, the initial mass is somewhere between $ 8\times 5=40g $ and $ 16\times 5=80g. $
