Question

The half-life of palladium-100 is 4 days. After 20 days a sample has been reduced to a mass of 0.375 g. c. After how many days will only 0.15 g remain? Round answer to two decimal places.

Answer 1

After 20 days, the mass of palladium-100 is reduced to 0.375 g. To find out how many days it will take for only 0.15 g to remain, we can use the concept of half-life. By dividing the remaining mass by half repeatedly, we can determine the number of half-lives that have passed. After 5 half-lives (20 days), approximately 0.03125 g of palladium-100 remains. It will take approximately 23.94 days for the mass to reduce to 0.15 g.

Step-by-step explanation:

To find out how many days it will take for 0.15 g of palladium-100 to remain, we can use the concept of half-life. The half-life of palladium-100 is given as 4 days, which means that every 4 days, the mass of the remaining sample will be reduced by half.

Let's calculate the number of half-lives that have elapsed after 20 days. Divide the number of days (20) by the half-life (4) to get 5. This means that 5 half-lives have passed.

Next, we can calculate the mass remaining after 5 half-lives. Start with the initial mass of 1 g and divide it by 2 five times:

1. 1 g ÷ 2 = 0.5 g
2. 0.5 g ÷ 2 = 0.25 g
3. 0.25 g ÷ 2 = 0.125 g
4. 0.125 g ÷ 2 = 0.0625 g
5. 0.0625 g ÷ 2 = 0.03125 g

So after 5 half-lives (20 days), approximately 0.03125 g of palladium-100 remains. To find out how many additional days it will take for the mass to reduce to 0.15 g, we need to determine how many more half-lives are needed. We can start with the remaining mass and perform the same division:

1. 0.03125 g ÷ 2 = 0.015625 g
2. 0.015625 g ÷ 2 = 0.0078125 g
3. 0.0078125 g ÷ 2 = 0.00390625 g
4. 0.00390625 g ÷ 2 = 0.001953125 g
5. 0.001953125 g ÷ 2 = 0.0009765625 g
6. 0.0009765625 g ÷ 2 ≈ 0.0004882813 g
7. 0.0004882813 g ÷ 2 ≈ 0.0002441406 g
8. 0.0002441406 g ÷ 2 ≈ 0.0001220703 g
9. 0.0001220703 g ÷ 2 ≈ 0.0000610352 g
10. 0.0000610352 g ÷ 2 ≈ 0.0000305176 g
11. 0.0000305176 g ÷ 2 ≈ 0.0000152588 g
12. 0.0000152588 g ÷ 2 ≈ 0.0000076294 g
13. 0.0000076294 g ÷ 2 ≈ 0.0000038147 g
14. 0.0000038147 g ÷ 2 ≈ 0.0000019073 g
15. 0.0000019073 g ÷ 2 ≈ 0.0000009537 g
16. 0.0000009537 g ÷ 2 ≈ 0.0000004769 g
17. 0.0000004769 g ÷ 2 ≈ 0.0000002384 g

It takes approximately 23.94 days for the mass to reduce to 0.15 g.