Calculate the haIf-life of bismuth-214 which has a decay constant of 4.3 x 10^3 s-1.
Correct answer: D. 1.6 x 10^-4 s
- A. 3.9 x 10^3 s
- B. 2.9 x 10^-1 s
- C. 2.9 x 10^3 s
- D. 1.6 x 10^-4 s
Explanation
decay constant = 4.3 x 103 s-1 t1/2 = ? t1/2 = 0.693 / decay constant t1/2 = 0.693 / 4.3 x 103 t1/2 = 1.6 x 10-4 s . Tip: As the numerator in the equation is less than 1 and is much smaller than the denominator, the value of t1/2 will never be greater than one. So cancel out the options with positive powers of 10 (a and c). To find out the correct option from the remaining 2 options find the sum of the powers. The numerator can be written as 6.93 x 10-1 and the denominator is x 103. Because the powers are dividing, therefore, the power of 10 of the final answer will be -1 - 3 = -4. Option D has x 10-4.
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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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