A rare isotope of a nuclear material is very​ unstable, decaying at a rate of 12% each second. Find how much isotope remains 14 seconds after 6 grams of the isotope is created. Round the amount to one decimal place.

Question

The mass of the remaining isotope is approximately 5.0 grams

The mass of the remaining isotope is approximately 1.1 grams.

The mass of the remaining isotope is approximately 29.3 grams

The mass of the remaining isotope is approximately 1.0 gram.

Answer 1

To find the amount of isotope remaining, we can use the formula:

Amount remaining = Initial amount * (1 - decay rate)^time

In this case, the initial amount is 6 grams, the decay rate is 12% or 0.12, and the time is 14 seconds.

Amount remaining = 6 * (1 - 0.12)^14
Amount remaining = 6 * (0.88)^14
Amount remaining ≈ 6 * 0.45
Amount remaining ≈ 2.7 grams

So, the correct answer is: The mass of the remaining isotope is approximately 2.7 grams.

Answer 2

is that correct?

Answer 3

I apologize for the incorrect response. Let's recalculate the correct answer:

Amount remaining = Initial amount * (1 - decay rate)^time

In this case, the initial amount is 6 grams, the decay rate is 12% or 0.12, and the time is 14 seconds.

Amount remaining = 6 * (1 - 0.12)^14
Amount remaining = 6 * (0.88)^14
Amount remaining ≈ 6 * 0.162
Amount remaining ≈ 0.972 grams

So, the correct answer is: The mass of the remaining isotope is approximately 0.972 grams.