The Half-life of radium is 1600 years. Which of the following is the fraction of a sample of radium that would remain un-decayed after 6400 years?
Correct answer: D. 1/16
- A. 1/2
- B. 1/4
- C. 1/8
- D. 1/16
Explanation
The half-life of radium is 1600 years. This means that after 1600 years, half of the radium atoms in a sample will have decayed. After 2 half-lives, or 3200 years, 1/4 of the radium atoms will have decayed. After 3 half-lives, or 4800 years, 1/8 of the radium atoms will have decayed. After 4 half-lives, or 6400 years, 1/16 of the radium atoms will have decayed. The fraction of the sample that would remain undecayed is given by the following formula: f = (1/2)^n
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About Half-life and Rate of Decay
Half-life is the time required for half the unstable nuclei in a sample to decay, and it remains constant for a particular radioactive nuclide. Questions use the exponential decay law, decay constant, activity, remaining quantity and mean life. Radioactive decay is random for individual nuclei but predictable for large samples.
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