IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.
Sagot :
To determine how much cesium remains from a 10 g sample after 6 years, given that cesium has a half-life of 2 years, we need to follow these steps:
1. Understand the Half-Life Concept:
The half-life is the amount of time it takes for half of a substance to decay. For cesium, this is 2 years.
2. Calculate the Number of Half-Lives:
We need to determine how many half-lives have passed in 6 years.
[tex]\[ \text{Number of half-lives} = \frac{\text{Time elapsed}}{\text{Half-life}} \][/tex]
Given:
[tex]\[ \text{Time elapsed} = 6 \text{ years} \][/tex]
[tex]\[ \text{Half-life} = 2 \text{ years} \][/tex]
[tex]\[ \text{Number of half-lives} = \frac{6}{2} = 3 \][/tex]
So, 3 half-lives have passed in 6 years.
3. Determine the Remaining Amount of Cesium:
For each half-life, the amount of the substance reduces by half. Starting with an initial amount of 10 g, we need to halve this amount three times due to the three half-lives that have passed.
- After the first half-life:
[tex]\[ 10 \text{ g} \times \frac{1}{2} = 5 \text{ g} \][/tex]
- After the second half-life:
[tex]\[ 5 \text{ g} \times \frac{1}{2} = 2.5 \text{ g} \][/tex]
- After the third half-life:
[tex]\[ 2.5 \text{ g} \times \frac{1}{2} = 1.25 \text{ g} \][/tex]
So, after 6 years (which is equivalent to three half-lives), the remaining amount of cesium is [tex]\(1.25\)[/tex] g.
Therefore, the correct answer is:
D. [tex]\(1 \frac{1}{4} \text{ g}\)[/tex]
1. Understand the Half-Life Concept:
The half-life is the amount of time it takes for half of a substance to decay. For cesium, this is 2 years.
2. Calculate the Number of Half-Lives:
We need to determine how many half-lives have passed in 6 years.
[tex]\[ \text{Number of half-lives} = \frac{\text{Time elapsed}}{\text{Half-life}} \][/tex]
Given:
[tex]\[ \text{Time elapsed} = 6 \text{ years} \][/tex]
[tex]\[ \text{Half-life} = 2 \text{ years} \][/tex]
[tex]\[ \text{Number of half-lives} = \frac{6}{2} = 3 \][/tex]
So, 3 half-lives have passed in 6 years.
3. Determine the Remaining Amount of Cesium:
For each half-life, the amount of the substance reduces by half. Starting with an initial amount of 10 g, we need to halve this amount three times due to the three half-lives that have passed.
- After the first half-life:
[tex]\[ 10 \text{ g} \times \frac{1}{2} = 5 \text{ g} \][/tex]
- After the second half-life:
[tex]\[ 5 \text{ g} \times \frac{1}{2} = 2.5 \text{ g} \][/tex]
- After the third half-life:
[tex]\[ 2.5 \text{ g} \times \frac{1}{2} = 1.25 \text{ g} \][/tex]
So, after 6 years (which is equivalent to three half-lives), the remaining amount of cesium is [tex]\(1.25\)[/tex] g.
Therefore, the correct answer is:
D. [tex]\(1 \frac{1}{4} \text{ g}\)[/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.