It would take 750 seconds for 8.0g of Polonium-214 to decay to 0.25g, using the concept of half-life which is 150 seconds for Polonium-214.
To calculate how long it will take for 8.0g of Polonium-214 to decay to 0.25g, we need to understand the concept of half-life, which is the time it takes for one-half of a given amount of a radioactive isotope to decay. Polonium-214 has a half-life of 150 seconds.
We can determine the number of half-lives needed for 8.0g to decay to 0.25g by dividing the final mass by the initial mass and then taking the logarithm base 2, as the process is exponential.
Here's the calculation:
Determine the number of half-lives needed for 8.0g to decay to 0.25g:
(0.25g / 8.0g) = 1/32, which is 2-5.
Calculate the number of half-lives (n):
n = log2(1/32) = -5.
Multiply the number of half-lives by the half-life duration:
-5 half-lives * 150 seconds/half-life = -750 seconds.
Since time cannot be negative, we take the absolute value, which is 750 seconds. It would take 750 seconds for 8.0g of Polonium-214 to decay to 0.25g.
Complete question:
Polonium-214 has a relatively short half-life of 150 seconds. How many seconds would it take for 8,0 g of this isotope to decay to 0.25 g?