Determine the mean lifetime of a radioactive atom characterized by a half-life of T?
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Answer: A. 1.44 T
Explanation
The mean lifetime of a radioactive atom is mathematically equal to the inverse of its decay constant. The decay constant is related to the half life by dividing the natural logarithm of two. Dividing one by the decay constant yields approximately 1.44 multiplied by the radionuclide half life. Radioactive decay follows a strict exponential decrease governed by a characteristic decay constant for each isotope. Half-life represents the exact duration required for exactly half of a given radioactive sample to decay. Mean lifetime represents the statistical average survival time for an individual radioactive atom before undergoing decay.
Option b incorrectly represents a fraction rather than the proper inverse logarithmic multiplication factor. Option c overestimates the proportionality constant by an incorrect decimal place in the decay formula. Option d mistakenly doubles the half-life value instead of applying the proper exponential decay constant relationship.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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