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For radioactive isotope I131, the time required for 50% disintegration is 8 days. The time required for 99.9 % disintegration of 5.5g of I131 is ___?
- a)54 days
- b)67 days
- c)80 days
- d)110 days
Correct answer is option 'C'. Can you explain this answer?
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For radioactive isotope I131, the time required for 50% disintegration...
Radioactive Decay of I131
Radioactive decay is the process by which a radioactive isotope undergoes a spontaneous transformation into one or more different nuclei. In this process, the unstable nucleus emits ionizing radiation, which can be in the form of alpha, beta, or gamma rays. The rate of radioactive decay is measured by the half-life (t1/2), which is the time required for half of the original sample to decay.
Given Information
- Half-life of I131 = 8 days
- 50% disintegration time = 8 days
- 99.9% disintegration time = ?
Calculations
The half-life of I131 is 8 days, which means that after 8 days, half of the original sample will decay. Therefore, if we start with 5.5g of I131, after 8 days, we will have 2.75g of I131 left.
To calculate the time required for 99.9% disintegration, we need to use the following formula:
Nt = N0(1/2)^(t/t1/2)
where Nt is the final amount, N0 is the initial amount, t is the time, and t1/2 is the half-life.
In this case, we want to find the time required for 99.9% disintegration, which means we want to find the time when only 0.1% of the original sample is left.
Nt/N0 = (1/2)^(t/t1/2)
0.001 = (1/2)^(t/t1/2)
t/t1/2 = log2(0.001)
t = t1/2 * log2(1/0.001)
t = 8 * log2(1000)
t = 80 days
Therefore, the time required for 99.9% disintegration of 5.5g of I131 is 80 days.
Conclusion
In conclusion, the radioactive isotope I131 has a half-life of 8 days, and the time required for 99.9% disintegration of 5.5g of I131 is 80 days. This calculation shows the importance of understanding radioactive decay and its applications in various fields, including medicine, energy production, and environmental monitoring.
Radioactive decay is the process by which a radioactive isotope undergoes a spontaneous transformation into one or more different nuclei. In this process, the unstable nucleus emits ionizing radiation, which can be in the form of alpha, beta, or gamma rays. The rate of radioactive decay is measured by the half-life (t1/2), which is the time required for half of the original sample to decay.
Given Information
- Half-life of I131 = 8 days
- 50% disintegration time = 8 days
- 99.9% disintegration time = ?
Calculations
The half-life of I131 is 8 days, which means that after 8 days, half of the original sample will decay. Therefore, if we start with 5.5g of I131, after 8 days, we will have 2.75g of I131 left.
To calculate the time required for 99.9% disintegration, we need to use the following formula:
Nt = N0(1/2)^(t/t1/2)
where Nt is the final amount, N0 is the initial amount, t is the time, and t1/2 is the half-life.
In this case, we want to find the time required for 99.9% disintegration, which means we want to find the time when only 0.1% of the original sample is left.
Nt/N0 = (1/2)^(t/t1/2)
0.001 = (1/2)^(t/t1/2)
t/t1/2 = log2(0.001)
t = t1/2 * log2(1/0.001)
t = 8 * log2(1000)
t = 80 days
Therefore, the time required for 99.9% disintegration of 5.5g of I131 is 80 days.
Conclusion
In conclusion, the radioactive isotope I131 has a half-life of 8 days, and the time required for 99.9% disintegration of 5.5g of I131 is 80 days. This calculation shows the importance of understanding radioactive decay and its applications in various fields, including medicine, energy production, and environmental monitoring.
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For radioactive isotope I131, the time required for 50% disintegration...
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For radioactive isotope I131, the time required for 50% disintegration is 8 days. The time required for 99.9 % disintegration of 5.5g of I131 is ___?a)54 daysb)67 daysc)80 daysd)110 daysCorrect answer is option 'C'. Can you explain this answer?
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