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.
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.
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.
is that correct?
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.
To find the remaining amount of the isotope after 14 seconds, we need to calculate how much isotope remains after each second and then multiply that by 14 to calculate the total remaining amount.
Each second, the isotope decays at a rate of 12%, which means that 88% (100% - 12%) of the isotope remains after each second.
To calculate the remaining amount after 1 second, we can multiply the initial amount (6 grams) by 88%:
Remaining after 1 second = 6 grams * 0.88 = 5.28 grams (rounded to two decimal places)
To find the remaining amount after 2 seconds, we can multiply the remaining amount after 1 second by 88%:
Remaining after 2 seconds = 5.28 grams * 0.88 = 4.64 grams (rounded to two decimal places)
Continuing this pattern, we can find the remaining amount after 14 seconds:
Remaining after 14 seconds = (6 grams * 0.88)^14 = 1.1 grams (rounded to one decimal place)
Therefore, the correct answer is: The mass of the remaining isotope is approximately 1.1 grams.
To find how much isotope remains 14 seconds after 6 grams of the isotope is created, we need to calculate the decay of the material over the given time period.
The decay rate is given as 12% per second. This means that each second, 12% of the remaining isotope will decay.
To calculate the remaining isotope after a certain number of seconds, we can use the formula:
Remaining mass = Initial mass * (1 - decay rate/100)^number of seconds
Using the given values, the initial mass is 6 grams, the decay rate is 12%, and the number of seconds is 14.
Plugging these values into the formula, we get:
Remaining mass = 6 * (1 - 12/100)^14
Calculating this expression, we find that the remaining mass is approximately 1.0 gram.
Therefore, the correct answer is:
The mass of the remaining isotope is approximately 1.0 gram.