Static charge can interfere with the production of plastic products by attracting dust and dirt. to reduce it, manufacturers expose the area to polonium-210, which has a half-life of 138 days. How much of a 25.0-g sample will remain after one year (365 days)?

N = N0(1/2)t/T = (25)(1/2)365/138 ≈ 4.0 g
Would 4.0 g be correct?

yes. Good work.

Well, I must admit, you've got the numbers right! However, using polonium-210 to reduce static charge is a bit excessive, don't you think? I mean, who needs all that radiation just to prevent dust and dirt from sticking to plastic products?

But hey, if you're really determined to go down that radioactive path, then yes, approximately 4.0 grams of polonium-210 will remain after one year. Just be prepared for some serious side effects... like growing an extra limb or glowing in the dark. Safety first, my friend!

No, the calculations provided are not correct. To find out how much of the 25.0-g sample of polonium-210 will remain after one year, you need to use the equation for exponential decay:

N = N0 * (1/2)^(t/T)

Where:
N = Amount of sample remaining after time t
N0 = Initial amount of sample
t = Time
T = Half-life of the substance

Using the values given:
N0 = 25.0 g
t = 365 days (1 year)
T = 138 days (half-life of polonium-210)

Plugging the values into the equation:

N = 25.0 * (1/2)^(365/138)

Calculating the value will give you the correct answer.

Yes, your calculation of approximately 4.0 g remaining after one year is correct. Here's an explanation of how to calculate it:

To find how much of the sample remains after one year, you can use the formula for exponential decay:

N = N0(1/2)^(t/T)

Where:
N = Final amount remaining
N0 = Initial amount
t = Time elapsed
T = Half-life of the substance

In this case, the initial amount of the sample is 25.0 g, the time elapsed is 365 days, and the half-life of polonium-210 is 138 days.

Plugging these values into the formula, you get:

N = (25) * (1/2)^(365/138)

Evaluating this expression, you find that approximately 4.0 g remains after one year.

So, 4.0 g would be the correct amount of the 25.0-g sample that remains after one year.