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A sample contains 4.00 x 10⁹ Bq of polonium-210 (Po-210). Assuming the disintegration of Po-210 follows first-order kinetics with a rate constant of 1.833 yr⁻¹, calculate the amount of time required for 99% of the initial amount of polonium to decay.

User Chamnap
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Final answer:

To find the time for 99% decay of Po-210 following first-order kinetics with a rate constant of 1.833 yr⁻¹, we use the first-order decay equation and solve for time after calculating the natural logarithm of the remaining fraction of the substance.

Step-by-step explanation:

The decay of polonium-210 (Po-210) follows first-order kinetics, and we can use the first-order rate equation to calculate the time required for a given percentage of decay. Since the rate constant (k) is given as 1.833 yr⁻¹, and we are looking for the time (t) required for 99% of the polonium to decay, we will use the equation:

ln(N_t/N_0) = -kt

where:

  • N_t is the remaining amount of substance at time t
  • N_0 is the initial amount of substance
  • k is the rate constant
  • t is the time

For a 99% decay, 1% of the substance remains, so N_t/N_0 is 0.01. We plug the values into the equation to solve for t:

ln(0.01) = -1.833 yr⁻¹ * t

t = ln(0.01) / -1.833 yr⁻¹

After calculating, we find the time t required for 99% decay of Po-210.

It's important to be aware that first-order decay is characterized by a rate of disintegration that is directly proportional to the amount of the substance present at any given time.

User Tarun Singhal
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