The half-life of a radioactive element is 10 hours. The fraction of initial radioactivity of the element that will remain after 40 hours is
Correct answer: B. 1/16
- A. 1/2
- B. 1/16
- C. 1/8
- D. 1/4
Explanation
Understand the concept of half-life: The half-life of a radioactive element is the time it takes for half of the original nuclei to decay.Calculate the number of half-life cycles:We are given the initial half-life (t_1/2) as 10 hours and the elapsed time (t) as 40 hours.Divide the elapsed time by the half-life to find the number of half-life cycles (n):n = t / t_1/2 = 40 hours / 10 hours = 4 cyclesApply the radioactive decay formula:The fraction of the remaining activity (R) after n half-life cycles is given by:R = (1/2)^nCalculate the remaining activity:Substitute the number of cycles (n) into the formula:R = (1/2)^4 = 1/16
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