In an experiment count rate of a sample of a radioactive element tale from 400 counts per second to 50 counts per second in 50 minutes. What is the half-life of radioactive element?
Correct answer: C. 50 minutes
- A. 30 minutes
- B. 40 minutes
- C. 50 minutes
- D. 60 minutes
Explanation
To determine the half-life of a radioactive element, we can use the formula for exponential decay:Nt = No × (½)^(t / T½)Nt is the count rate at time tNo is the initial count rate.T½ is the half-life of the radioactive elementGiven that:No = 400 counts per secondNt = 50 counts per secondt = 50 minutesPutting values in the above equation:50 = 400 × (½)^(150 / T½)Dividing both sides of the equation by 400:⅛ = (½)^(150 / T½)Taking the logarithm (base 2)of both sides:-3 = (150 / T½) × log2(½)Simplifying:-3 = -150 / T½Cross-multiplying:T½ = 150/3= 50 minutesTherefore, the half-life of the radioactive element is 50 minutes.
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