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The half-life of a radioactive element is 30 min. The time interval between the stages of 33.3% and 67.7% decay will be (in min): [rounded up to first decimal place]
Correct answer is between '29.0,31.0'. Can you explain this answer?
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The half-life of a radioactive element is 30 min. The time interval be...
**Half-Life and Decay**
The half-life of a radioactive element is the time it takes for half of the radioactive substance to decay. In this case, the half-life is given as 30 minutes. This means that after 30 minutes, half of the radioactive substance will have decayed, and after another 30 minutes, half of the remaining substance will have decayed, and so on.
**Calculating the Time Interval**
To calculate the time interval between the stages of 33.3% and 67.7% decay, we need to find the time it takes for the radioactive substance to decay from 33.3% to 67.7%.
First, let's determine the fraction of the substance that remains after 33.3% decay. If the original amount is represented by 100%, then 33.3% decay means that 66.7% of the substance remains (100% - 33.3% = 66.7%).
Next, let's determine the fraction of the substance that remains after 67.7% decay. If the original amount is represented by 100%, then 67.7% decay means that 32.3% of the substance remains (100% - 67.7% = 32.3%).
Now, we need to find the time it takes for the radioactive substance to decay from 66.7% to 32.3%. Since we know the half-life is 30 minutes, we can divide this time interval into two equal parts.
**Calculating the First Part of the Time Interval**
To calculate the first part of the time interval, we need to find the time it takes for the remaining fraction of the substance to decay from 66.7% to 50%. Since half of the substance has already decayed, we are left with half of the remaining substance. This means that the remaining fraction is now 50%.
Since the half-life is 30 minutes, it takes 30 minutes for the remaining fraction to decay from 66.7% to 50%.
**Calculating the Second Part of the Time Interval**
Now, we need to find the time it takes for the remaining fraction of the substance to decay from 50% to 32.3%. Again, we are dealing with half of the remaining substance, so the remaining fraction is now 50% of 50%, which is 25%.
Using the half-life of 30 minutes, it takes another 30 minutes for the remaining fraction to decay from 50% to 25%.
**Calculating the Total Time Interval**
To find the total time interval, we add the time calculated for the first part and the second part of the time interval.
30 minutes (for the first part) + 30 minutes (for the second part) = 60 minutes.
Therefore, the time interval between the stages of 33.3% and 67.7% decay is 60 minutes. Since we were asked to round up to the first decimal place, the correct answer is between 29.0 and 31.0 minutes.
The half-life of a radioactive element is the time it takes for half of the radioactive substance to decay. In this case, the half-life is given as 30 minutes. This means that after 30 minutes, half of the radioactive substance will have decayed, and after another 30 minutes, half of the remaining substance will have decayed, and so on.
**Calculating the Time Interval**
To calculate the time interval between the stages of 33.3% and 67.7% decay, we need to find the time it takes for the radioactive substance to decay from 33.3% to 67.7%.
First, let's determine the fraction of the substance that remains after 33.3% decay. If the original amount is represented by 100%, then 33.3% decay means that 66.7% of the substance remains (100% - 33.3% = 66.7%).
Next, let's determine the fraction of the substance that remains after 67.7% decay. If the original amount is represented by 100%, then 67.7% decay means that 32.3% of the substance remains (100% - 67.7% = 32.3%).
Now, we need to find the time it takes for the radioactive substance to decay from 66.7% to 32.3%. Since we know the half-life is 30 minutes, we can divide this time interval into two equal parts.
**Calculating the First Part of the Time Interval**
To calculate the first part of the time interval, we need to find the time it takes for the remaining fraction of the substance to decay from 66.7% to 50%. Since half of the substance has already decayed, we are left with half of the remaining substance. This means that the remaining fraction is now 50%.
Since the half-life is 30 minutes, it takes 30 minutes for the remaining fraction to decay from 66.7% to 50%.
**Calculating the Second Part of the Time Interval**
Now, we need to find the time it takes for the remaining fraction of the substance to decay from 50% to 32.3%. Again, we are dealing with half of the remaining substance, so the remaining fraction is now 50% of 50%, which is 25%.
Using the half-life of 30 minutes, it takes another 30 minutes for the remaining fraction to decay from 50% to 25%.
**Calculating the Total Time Interval**
To find the total time interval, we add the time calculated for the first part and the second part of the time interval.
30 minutes (for the first part) + 30 minutes (for the second part) = 60 minutes.
Therefore, the time interval between the stages of 33.3% and 67.7% decay is 60 minutes. Since we were asked to round up to the first decimal place, the correct answer is between 29.0 and 31.0 minutes.
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The half-life of a radioactive element is 30 min. The time interval be...
T(1/2)= .693/k again , t(33.3%) =ln {100 /66.7} /k and t(66.7%) =ln {100/33.3}/ k or, t(66.7%) - t(33.3%) = 1/k × {ln 3/1 - ln 3/2} or, t(66.7%) - t (33.3%) = 1/k × ln { 3/1 × 2/3}. or, t(66.7%) - t (33.3%) = 1/k × ln2. or, t(66.7% ) - t (33.3%) = .693/k = t(1/2) = 30 min...
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The half-life of a radioactive element is 30 min. The time interval between the stages of 33.3% and 67.7% decay will be (in min): [rounded up to first decimal place]Correct answer is between '29.0,31.0'. Can you explain this answer?
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