The half-life of polonium-218 is 3.0 minutes. If you start with 30.0 g, how long will it be before only 1.1 g remains?
Any idea how to get started on this?
To determine how long it will take for only 1.1 g of polonium-218 to remain, we need to use the concept of half-life. The half-life is the amount of time it takes for half of a radioactive substance to decay.
Given that the half-life of polonium-218 is 3.0 minutes, we can use this information to find the time required for the remaining amount to reach 1.1 g.
Let's break down the steps:
1. Start with 30.0 g of polonium-218.
2. The first half-life would decrease the original amount by half, leaving 15.0 g after 3.0 minutes.
3. The second half-life would again decrease the amount by half, leaving 7.5 g after another 3.0 minutes.
4. The third half-life would result in 3.75 g remaining, and so on.
We can continue this process until we reach the desired amount of 1.1 g.
Here's the calculation:
30.0 g - 15.0 g - 7.5 g - 3.75 g - 1.875 g - 0.9375 g - 0.46875 g - 0.234375 g - 0.1171875 g - 0.05859375 g - 0.02929688 g - 0.01464844 g - 0.00732422 g - 0.00366211 g - 0.00183105 g - 0.00091553 g - 0.00045776 g - 0.00022888 g - 0.00011444 g - 0.00005722 g - 0.00002861 g - 0.00001431 g - 0.00000715 g - 0.00000357 g - 0.00000179 g - 0.00000089 g - 0.00000044 g - 0.00000022 g
When we round up to the nearest minute, after approximately 21 minutes, only 1.1 g of polonium-218 will remain.