The half-life of plutonium-234 is 9 hours. If 40 milligrams is present now, how much will be present in 4 days? (Round your answer to three decimal places.)

after h hours,

40 * (1/2)^(h/9)

That's because for every 9 hours, the amount is multiplied by 1/2

so, after 4 days = 96 hours, we will have

40 * (1/2)^(96/9) = .0246 mg

Well, plutonium-234 certainly has a short attention span! After 9 hours, it's already halfway gone! So let's calculate how much will be left after 4 days.

In 4 days, we have 96 hours. Divide that by the half-life of 9 hours, and you'll get 10.667.

Now, since it's half-life, we know that each time, we're losing half of the remaining amount. So, raise 0.5 to the power of 10.667, and you'll get approximately 0.007.

Multiply that by the initial amount of 40 milligrams, and you'll find that approximately 0.28 milligrams of plutonium-234 will be present in 4 days.

So, the answer is approximately 0.280 milligrams. But don't worry, it won't disappear in a cloud of smoke with a little "poof" sound!

To calculate the amount of plutonium-234 present in 4 days, we need to determine how many half-lives occur in that time period.

Since the half-life of plutonium-234 is 9 hours, we know that after 9 hours, half of the original amount will remain. This means that in 4 days (or 96 hours), the number of half-lives would be 96 / 9 = 10.667 (rounded to three decimal places).

To calculate the amount of plutonium-234 remaining after this time period, we can use the formula:

Amount = Initial Amount * (1/2)^(number of half-lives)

So, the calculation would be:

Amount = 40 mg * (1/2)^(10.667)

Using a calculator, we get:

Amount ≈ 40 mg * 0.000755

Amount ≈ 0.0302 mg

Therefore, approximately 0.0302 milligrams of plutonium-234 will be present after 4 days.

To answer this question, we need to understand what half-life means. The half-life of a substance is the time it takes for half of the original amount to decay or disappear.

In this case, the half-life of plutonium-234 is given as 9 hours. This means that after 9 hours, half of the initial amount will decay.

Now, let's calculate the number of half-lives in 4 days (which is equivalent to 96 hours):

Number of half-lives = (Total time elapsed) / (Half-life)
Number of half-lives = 96 hours / 9 hours = 10.667

So, after 4 days, there would be approximately 10.667 half-lives.

To calculate the amount of plutonium-234 remaining after 4 days, we can use the following formula:

Amount remaining = Initial amount * (1/2)^(Number of half-lives)

Substituting the given values:

Amount remaining = 40 mg * (1/2)^(10.667)

Now, let's calculate the amount remaining:

Amount remaining = 40 mg * (0.5)^(10.667)
Amount remaining = 40 mg * 0.000618475
Amount remaining = 0.024738 mg (rounded to three decimal places)

Therefore, approximately 0.025 milligrams of plutonium-234 will be present after 4 days.