Po-218 is an alpha emitter with a half-life of 3.0 minutes. If a sample contains 56 mg of Po-218, how many alpha emissions would occur in 6.0 minutes?

I got 2.4e20 but it said it was wrong. I did what my teacher showed us to do.

My work:

86(i got this by diving 100/2/2 then subtracting that from 100) X 1g/1000/mg X 6.022e23amu/1g X 1 atom/218 amu X 1 alpha particle/1 atom

what am i doing wrong?

http://www.jiskha.com/display.cgi?id=1286326760

Use your numbers, not those in DrBob's example.

thanks.

um..wait i think i get everything except how do you calculate the molar mass?

Doesn't Po-218 tell you the molar mass is 218?

It seems like you have made a slight error in your calculation. Let's go through the problem step by step to identify the mistake.

First, we need to convert the given mass of Po-218 from milligrams to grams. Since there are 1000 milligrams in a gram, we divide 56 mg by 1000 to get 0.056 grams.

Next, we can calculate the number of atoms of Po-218 in the sample by using Avogadro's number, which is 6.022 × 10^23 atoms/mol. We can set up a conversion factor as follows:

0.056 g Po-218 × (1 mol Po-218 / 218 g) × (6.022 × 10^23 atoms / 1 mol) = X atoms (where X is the number of atoms)

By simplifying the units, we find:

0.056 / 218 × (6.022 × 10^23) = X

Now we can find the number of alpha emissions in 6.0 minutes by considering the half-life of Po-218. Since the half-life is 3.0 minutes, we can divide the total time (6.0 minutes) by the half-life:

6.0 minutes / 3.0 minutes = 2

So, in 6.0 minutes, there will be 2 half-life periods.

Now, we know that each half-life period corresponds to one-half of the original amount of radioactive material decaying. Therefore, the number of remaining atoms after 2 half-life periods is (1/2)^(2) times the initial number of atoms.

To find the number of alpha emissions, we can subtract the remaining atoms from the initial number of atoms and multiply it by the number of alpha particles emitted per decay.

However, your calculations seemed to be focused on determining the total number of alpha particles emitted by one atom of Po-218, rather than the total number of emissions from a given sample over a specific time period. This is likely the cause of the discrepancy in your answer.

I hope this explanation helps you understand the problem and how to correctly solve it.