For this problem. We're being asked to figure out how many Alfa emissions occur in 25 minutes from polonium 2 18 which has 1/2 life of three minutes. If we have a sample of 55 milligrams which has on that polonium 2 18 has an atomic mass of to 18.8965 a m. U. Um, And then we're also being asked to figure out what that dose of radiation is in Curie. So first thing we have to do is figure out our, um are rate constants. Okay, Um And to do that, we're going to go ahead and switch these minutes into seconds. So, um, three times 60. It's gonna turn our minutes in two seconds. This is 180 seconds. And for our 25 minutes, we're gonna get there That's 1500 stuck in. The reason we're doing that is because we want to have it in seconds later when we have to determine Arcuri. Okay, so first off to find Kay, we're going to rearrange our equation here, but we'll have our half. Life is 180 seconds equals zero point 693 divided by K. And we find that K comes out to be 3.8508 times 10 to the negative. Third per second. Um, now we can go in the head and figure out from there. How much? Um, mass is remaining at time equals 25 minutes. Um, And to do that, we're gonna use this equation here, so and start off with the natural log of and t divided by 55 milligrams equals negative. Three point 8508 times 10 to the negative. Third time time, which is 1500 seconds, um, to rearrange and solve for anti. We're gonna take the inverse here. So? So this will, under being anti equals 55 the inverse negative 3.8508 times 10 to the negative. Third times 1500. And we get that are the mass after is going to equal zero point 1705 three milligrams. So that's how much is left after decay. So to figure out how much has decayed, we have to subtract that from our original value. So we're gonna 55 minus 0.17053 now we get that 54.8 to 947 milligrams decayed. Now to figure out the emissions, we're going to take that value. The how many have decayed, how many milligrams decayed and converted into Adam's. So we will take this 55 or 54 0.8 to 947 and multiply that by one mole of, um, polonium to 18 is equal to, uh, to 18.8 965 grams of polonium 2 18 and then multiply that by 6.22 times 10 to the 23rd Adams her mole, Um, and we get that there were a total of for one point 514 five times, 10 to the 20th Adams of polonium to 18. That's how many Adams were admitted during that time span. So to find the rate, we will now take that value 1.5145 times tend to the 20th and divide that by our time span, which is 50 hunt 1500 seconds, and we come out with 1.97 times, 10 to the 17th Adams of polonium 2 18 per second. Now the last part of this question is asking us to take that and figure out what that the dosage isn't is in Curie's. So we will take this value this 1.97 times, turning to the 17th her second. Multiply that by one Curie emitted Um, divided by 3.7 times, turned to the 10th stuck in per second, and we get that that is 2.7 times 10 to this six Curie's admit it.